TOREADOR ROYALTY CORP
SC 13D/A, 1998-12-23
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13D

                    Under the Securities Exchange Act of 1934
                                (AMENDMENT NO. 7)


                          Toreador Royalty Corporation
- --------------------------------------------------------------------------------
                                (Name of Issuer)

                   Common Stock, par value $0.15625 per share
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    891041105
- --------------------------------------------------------------------------------
                                 (CUSIP Number)

                             Janice V. Sharry, Esq.
                              Haynes and Boone, LLP
                           901 Main Street, Suite 3100
                               Dallas, Texas 75202
                                 (214) 651-5562
- --------------------------------------------------------------------------------
       (Name, Address and Telephone Number of Person Authorized to Receive
                           Notices and Communications)

                               December 16, 1998
- --------------------------------------------------------------------------------
            (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition that is the subject of this Schedule 13D, and is filing this
schedule because of Sections 240.13d-1(e), (f) or (g), check the following box 
[ ].

Note: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Section 240.13d-7(b) for
other parties to whom copies are to be sent.

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).


<PAGE>   2
                                  SCHEDULE 13D

CUSIP NO. 891041105

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    Lee Global Energy Fund, L.P.
    75-2569264
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [X]
                                                                        (b) [ ]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS

    WC
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

    N/A
- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION

    Texas
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           899,650
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          0
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    899,650
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    0
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,321,450
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES                                                         [ ]

     N/A
- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     24.4%(1)
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON

     PN
- --------------------------------------------------------------------------------

(1)    Based on 5,160,671 shares of Common Stock issued and outstanding as of
       September 30, 1998, as disclosed in the Issuer's Form 10-Q for the
       quarter ended September 30, 1998 plus the assumed conversion of Series A
       Convertible Preferred Stock issued to William I. Lee into 250,000 shares
       of Common Stock.
<PAGE>   3
                                  SCHEDULE 13D

CUSIP NO. 891041105

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    G. Thomas Graves III
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
                                                                        (a) [X]
                                                                        (b) [ ]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS

    PF
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                  

    N/A
- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION

    U.S.
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           20,000
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          977,250 (2)
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    20,000
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    977,250 (2)
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,321,450
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES                                                        [ ]

     N/A
- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     24.4%(1)
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON

     IN
- --------------------------------------------------------------------------------

(1)    Based on 5,160,671 shares of Common Stock issued and outstanding as of
       September 30, 1998, as disclosed in the Issuer's Form 10-Q for the
       quarter ended September 30, 1998 plus the assumed conversion of Series A
       Convertible Preferred Stock issued to William I. Lee into 250,000 shares
       of Common Stock.

(2)    Mr. Graves may be deemed to have shared voting power and shared 
       dispositive power over 899,650 Shares owned by Lee Global Energy Fund, 
       L.P. for whom Mr. Graves serves as managing general partner and 77,600 
       Shares owned by Wilco Properties, Inc., for whom Mr. Graves serves as 
       President and Chief Operating Officer.
<PAGE>   4
                                  SCHEDULE 13D

CUSIP NO. 891041105

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    William I. Lee
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [X]
                                                                        (b) [ ]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS

    PF
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

    N/A
- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION

    U.S.
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           324,200(2)
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          977,250 (3)
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    324,200(2)
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    977,250 (3)
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,321,450
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES                                                         [ ]

     N/A
- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     24.4%(1)
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON

     IN
- --------------------------------------------------------------------------------

(1)  Based on 5,160,671 shares of Common Stock issued and outstanding as of
     September 30, 1998, as disclosed in the Issuer's Form 10-Q for the quarter
     ended September 30, 1998 plus the assumed conversion of Series A
     Convertible Preferred Stock issued to William I. Lee into 250,000 shares of
     Common Stock.

(2)  Includes 250,000 shares issuable upon conversion of shares of Series A
     Convertible Preferred Stock held by William I. Lee.

(3)  Mr. Lee may be deemed to have shared voting power and shared
     dispositive power over 899,650 shares owned by Lee Global Energy Fund, L.P.
     and 77,600 shares owned by Wilco Properties, Inc.
<PAGE>   5
                                  SCHEDULE 13D

CUSIP NO. 891041105

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    Wilco Properties, Inc.
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
                                                                        (a) [X]
                                                                        (b) [ ]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS

    WC
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

    N/A
- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION

    Texas
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           77,600
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          0
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    77,600
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    0
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,321,450
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES                                                         [ ]

     N/A
- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     24.4%(1)
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     CO
- --------------------------------------------------------------------------------

(1)  Based on 5,160,671 shares of Common Stock issued and outstanding as of
     September 30, 1998, as disclosed in the Issuer's Form 10-Q for the quarter
     ended September 30, 1998 plus the assumed conversion of Series A
     Convertible Preferred Stock issued to William I. Lee into 250,000 shares of
     Common Stock.


<PAGE>   6
     This Amendment No. 7 to Schedule 13D (this "Amendment") amends and
supplements the Amendment No. 6 to Schedule 13D filed by Lee Global Energy Fund,
L.P. (the "Fund") et al., by furnishing the information set forth below. Unless
set forth below, all previously reported Items are unchanged.

Item 3.  Source and Amount of Funds or Other Consideration.

       Item 3 is hereby supplemented as follows:

       The total amount of funds required by Lee for the purchase of 40,000
shares of the Issuer's Series A Convertible Preferred Stock (convertible into an
aggregate of 250,000 Shares) was approximately $1,000,000 and was obtained from
personal funds.

Item 5.  Interest in Securities of the Issuer.

       Item 5 is hereby amended in its entirety as follows:

       (a) Pursuant to that certain Joint Filing Agreement, entered into by and
among the Fund, Graves, Lee and Wilco, dated as of September 18, 1998
(previously filed as Exhibit 7.9 and incorporated herein by reference), each of
the Fund, Graves, Lee and Wilco may be deemed to beneficially own 1,321,450
Shares (which is approximately 24.4% of the Shares outstanding on September 30,
1998, as disclosed in the Issuer's Form 10-Q for the quarter ended September 30,
1998 plus the assumed conversion of Series A Convertible Preferred Stock issued
to Lee into 250,000 Shares). Mr. Graves may be deemed to have shared voting
power and shared dispositive power over 899,650 Shares owned by Lee Global
Energy Fund, L.P., for whom Mr. Graves serves as managing partner and 77,600
Shares of Wilco Properties, Inc., for whom Mr. Graves serves as President and
Chief Operating Officer. Mr. Lee may be deemed to have shared voting power and
shared dispositive power over 899,650 Shares owned by Lee Global Energy Fund
L.P. and 77,600 Shares owned by Wilco Properties, Inc.

       (b)

<TABLE>
<CAPTION>
                                 Sole              Shared            Sole             Shared
                                 Voting            Voting            Dispositive      Dispositive
                                 Power             Power             Power            Power
                                 ----------------------------------------------------------------
<S>                              <C>               <C>               <C>              <C>
Lee Global Energy Fund, L.P.     899,650              0              899,650             0
G. Thomas Graves, III             20,000           977,250            20,000           977,250
William I. Lee                   324,200           977,250           324,200           977,250
Wilco Properties, Inc.            77,600              0               77,600             0
</TABLE>

     As a result of being a party to that certain Stockholder Agreement (a copy
of which was previously filed as Exhibit 7.5 to Amendment No. 4 to Schedule 13D
and is incorporated herein by reference), entered into by and among the Fund,
Graves, Lee, Gralee Partners and the General Partner; Mr. Peter Lawrence Falb,
Mr. Edward Nathan Dane, Firethorn I Limited Partnership, the Hilary Bell Falb
1983 Trust, the Alison Forslund Falb 1985 Trust, the Forslund Irrevocable Trust,
and Dane, Falb, Stone & Co., Inc. (collectively referred to as the "Dane Falb
Persons"); and Mr. John V. Ballard, Mr. J. W. Bullion, Mr. Thomas P. Kellogg,
Jr., Mr. John Mark McLaughlin, Mr. Peter R. Vig, and Mr. Jack L. Woods, the
Fund, Graves and Lee may each be deemed to have indirect beneficial ownership
of, and shared voting power with respect to, an additional 27.7% (assuming the
conversion of all Series A Convertible Preferred Stock owned by each of Mr.
Falb, Mr. McLaughlin and 


<PAGE>   7
Mr. Kellogg) of the Company's Shares, consisting of 885,800 Shares
beneficially owned by the Dane Falb Persons (17.1%) (as represented in their
Schedule 13D/A filed with the Securities and Exchange Commission on July 30,
1998 plus an additional 2,500 Shares as represented in Mr. Falb's Form 4 dated
November 12, 1998, plus personal knowledge of Mr. Falb's purchase of Series A
Convertible Preferred Stock convertible into an additional 25,000 Shares and
assuming the conversion of only Mr. Falb's Series A Convertible Preferred
Stock), 222,924 Shares beneficially owned by Mr. John V. Ballard, Mr. J. W.
Bullion, Mr. Thomas P. Kellogg, Jr. and Mr. Jack L. Woods (4.3%) (as represented
in the Issuer's definitive proxy material filed with the Securities and Exchange
Commission on July 1, 1998, plus personal knowledge of Mr. Kellogg's purchase of
Series A Convertible Preferred Stock convertible into 25,000 Shares and assuming
the conversion of only Mr. Kellogg's Series A Convertible Preferred Stock),
353,036 Shares beneficially owned by Mr. John Mark McLaughlin (6.8%) (as
represented in his Schedule 13D filed with the Securities and Exchange
Commission on July 10, 1998, plus personal knowledge of Mr. McLaughlin's
purchase of Series A Convertible Preferred Stock convertible into 62,500 Shares
and assuming the conversion of only Mr. McLaughlin Series A Convertible
Preferred Stock), and no Shares beneficially owned by Mr. Peter R. Vig (0.0%)
(as represented in his Schedule 13D filed with the Securities and Exchange
Commission on August 7, 1998).

     (c) Since the filing of the previous Schedule 13D (Amendment No. 6), the
only transaction in the Shares by Lee was the purchase on December 9, 1998 of
40,000 Shares of Series A Convertible Preferred Stock convertible into 250,000
Shares. The purchase price for each share of Series A Convertible Preferred
Stock was $25.00 (aggregate purchase price of $1,000,000). The shares are
convertible into Shares at any time at a conversion price of $4.00 per Share.
Since the filing of the previous Schedule 13D (Amendment No. 6) the only
transactions in the Shares by Graves were the purchase on October 29, 1998, of
2,000 Shares for $2.44 per Share and the purchase on November 2, 1998, of 8,000
Shares for $2.41 per share. Since the filing of the previous Schedule 13D
(Amendment No. 6), Wilco has purchased 37,500 Shares. On October 2, 1998, Wilco
purchased 5,000 Shares for $2.55 per Share. On October 5, 1998 Wilco purchased
10,000 Shares for $2.55 per Share. On October 19, 1998, Wilco purchased 2,000
Shares for $2.49 per Share. On October 20, 1998, Wilco purchased 3,000 Shares
for $2.37 per Share. On October 22, 1998, Wilco Purchased 2,000 Shares for $2.05
per Share. On October 23, 1998, Wilco purchased 4,000 Shares for $2.30 per
Share. On November 3, 1998, Wilco purchased 6,000 Shares for $2.55 per Share. On
November 9, 1998, Wilco purchased 500 Shares for $3.17 per Share. On November
12, 1998, Wilco purchased 500 Shares for $3.32 per Share. On December 9, 1998,
Wilco purchased 1,000 Shares for $2.97 per Share. On December 16, 1998, Wilco
purchased 1,000 Shares for $2.85 per Share. On December 21, 1998, Wilco
purchased 2,500 Shares for $2.68 per Share. Since the filing of the previous
Schedule 13D (Amendment No. 6), the Fund has purchased 55,700 Shares. On
September 16, 1998, the Fund purchased 4,500 Shares for $2.77 per Share. On
September 18, 1998, the Fund purchased 10,000 Shares for $2.68 per Share. On
September 23, 1998, the Fund purchased 29,900 Shares for $2.80 per Share. On
December 1, 1998, the Fund purchased 2,000 Shares for $3.42 per Share. On
December 3, 1998, the Fund purchased 1,000 Shares for $3.80 per Share. On
December 7, 1998, the Fund purchased 7,300 Shares for $2.93 per Share. On
December 8, 1998, the Fund purchased 1,000 Shares for $2.97 per Share. The Fund
also distributed 60,000 Shares to one of its partners on October 1, 1998 when
the Shares were valued at $2.38 per Share. The Fund also pledged 190,900 Shares
as collateral for a loan on November 15, 1998.

     (d) No other person has any right to receive or the power to direct the
receipt of dividends from, or the proceeds from the sale of, the Shares with
respect to which this filing is made.

     (e) Not applicable.

Item 6.  Contracts, Arrangements, Understandings or Relationships With Respect
to Securities of the Issuer.

     Item 6 is hereby amended in its entirety as follows:

     Mr. Lee acquired 40,000 Shares of Series A Convertible Preferred Stock
convertible into 250,000 Shares (the "Preferred Stock") pursuant to a Securities
Purchase Agreement (attached hereto as Exhibit 7.10) effective December 16, 1998
by and among the Issuer and the Purchasers party thereto (the "SPA"). Under the
SPA, the Purchasers agreed to pay $25.00 per share of Preferred Stock. Each of
the parties made certain standard representations and warranties in the SPA.
Each Purchaser represented and warranted that he was an accredited investor as
defined by Rule 501(a) of Regulation D in the SPA.



<PAGE>   8
       In conjunction with the SPA, the parties entered into a Registration
Rights Agreement (attached hereto as Exhibit 7.11) effective December 16, 1998,
by and among the Issuer and the persons party thereto (the "RRA"). The RRA
obligates the Issuer to file a Registration Statement with respect to the Shares
reserved for conversion of the Preferred Stock on Form S-3 within 90 days of
demand by holders of 26% of the outstanding Series A Convertible Preferred
Stock. The RRA also contains a provision for piggyback registration. The Issuer
is obligated to prepare and file certain reports with the Securities and
Exchange Commission and to make "blue sky" filings where appropriate. 

       The rights, preferences, privileges and restrictions of the Preferred
Stock is set forth in the Certificate of Designation of Series A Preferred Stock
(attached hereto as Exhibit 7.12) (the "COD"). The COD provides for dividends
paid at 9% of Stated Value (Stated Value equals $25.00 per share of Preferred
Stock) which is payable, at the Issuer's option, in cash or in shares of Series
A Convertible Preferred Stock. Upon dissolution, the holders of Preferred Stock
have preference ahead of all holders of all other capital stock. The COD
provides that the holders of Preferred Stock may convert their shares into
Shares at any time at a rate equal to the Stated Value divided by the Conversion
Price ($4.00 per Share). The conversion rate is adjusted to account for stock
splits, stock dividends, mergers and similar transactions, under the COD. The
Issuer must redeem the Preferred Stock outstanding on December 1, 2008 at the
Stated Value and may redeem the stock at any time after December 1, 2001,
subject to certain conditions.

Item 7.  Material to be Filed as Exhibits.

       Item 7 is hereby supplemented as follows:

       7.10 Securities Purchase Agreement, effective December 16, 1998, among
the Issuer and the Purchasers party thereto.

       7.11 Registration Rights Agreement, effective December 16, 1998, among
the Issuer and the persons party thereto.

       7.12 Certificate of Designation of Series A Convertible Preferred Stock 
of Toreador Royalty Corporation.





<PAGE>   9
                                    SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.


Date:    December 22, 1998


                                         LEE GLOBAL ENERGY FUND, L.P.

                                         By: Gralee Partners, L.P., 
                                             its general partner

                                             By: Gralee Capital Corp., 
                                                 its general partner

                                                 By: /s/ G. THOMAS GRAVES III
                                                    ----------------------------
                                                     Name:  G. Thomas Graves III
                                                     Title: President


                                         /s/ G. THOMAS GRAVES III    
                                         ---------------------------------------
                                         G. THOMAS GRAVES III


                                         /s/ WILLIAM I. LEE             
                                         ---------------------------------------
                                         WILLIAM I. LEE



                                         WILCO PROPERTIES, INC.


                                         By: /s/ G. THOMAS GRAVES III
                                            ------------------------------------
                                         Name:  G. Thomas Graves III
                                         Title: President
<PAGE>   10
                                 EXHIBIT INDEX


<TABLE>
<CAPTION>
  EXHIBIT
  NUMBER              DESCRIPTION
  -------             -----------
  <S>          <C>
    7.10       Securities Purchase Agreement, effective December 16, 1998, among
               the Issuer and the Purchasers party thereto.

    7.11       Registration Rights Agreement, effective December 16, 1998, among
               the Issuer and the persons party thereto.

    7.12       Certificate of Designation of Series A Convertible Preferred 
               Stock of Toreador Royalty Corporation.
</TABLE>





<PAGE>   1
                                                                    EXHIBIT 7.10


                          SECURITIES PURCHASE AGREEMENT


         SECURITIES PURCHASE AGREEMENT (this "Agreement") by and among Toreador
Royalty Corporation, a Delaware corporation (the "Company"), and each of the
persons listed on the Schedule of Purchasers attached hereto. Such entities or
persons (and any other persons who become a party to this Agreement subsequent
to the date of this Agreement pursuant to Section 1.1) are each referred to
herein as a "Purchaser" and, collectively, as the "Purchasers".

         The Company wishes to sell to each Purchaser, and each Purchaser wishes
to buy, on the terms and subject to the conditions set forth in this Agreement,
shares (the "Preferred Shares") of the Company's Series A Convertible Preferred
Stock, par value $1.00 per share (the "Preferred Stock"). The Preferred Shares
are convertible pursuant to the terms of a Certificate of Designation relating
to the Preferred Stock, the form of which is attached hereto as Exhibit A (the
"Certificate of Designation") into shares (the "Conversion Shares") of the
Company's Common Stock, par value $0.15625 per share (the "Common Stock").
Dividends on the Preferred Shares are payable, subject to the terms and
conditions of the Certificate of Designation, in cash or, at the Company's
option, shares of Preferred Stock (the "Dividend Payment Shares"). The Preferred
Shares, the Conversion Shares, and the Dividend Payment Shares are collectively
referred to herein as the "Securities".

         The Company has agreed to effect the registration of the Conversion
Shares under the Securities Act of 1933, as amended (the "Securities Act"), upon
the occurrence of certain events set out in and pursuant to a Registration
Rights Agreement of even date herewith by and among the Company and the
Purchasers (the "Registration Rights Agreement"). The sale of the Preferred
Shares by the Company to the Purchasers will be effected in reliance upon the
exemption from securities registration afforded by the provisions of Regulation
D ("Regulation D"), as promulgated by the Securities and Exchange Commission
(the "Commission") under the Securities Act.

         The Company and the Purchasers hereby agree as follows:

1.       PURCHASE AND SALE OF PREFERRED SHARES.

         1.1   Agreement to Purchase and Sell. Upon the terms set forth herein,
the Company agrees to sell and each Purchaser agrees to purchase, the number of
Preferred Shares set forth below such Purchaser's name on the signature pages
hereof and at a purchase price equal to Twenty-Five Dollars ($25.00) times the
number of Preferred Shares purchased by such Purchaser (the "Purchase Price").
The Company may sell from time to time up to $4,000,000 of Preferred Shares,
provided, however, that at least $3,000,000 of Preferred Shares shall have been
purchased as of the date of the first sale of Preferred Shares pursuant to this
Agreement. Notwithstanding any provision of this Agreement to the contrary, the
Company may from time to time after the date of this Agreement sell, without any
consent or acknowledgment of the Purchasers signatory hereto, additional
Preferred Shares (not to exceed the $4,000,000 limitation set forth in the
preceding sentence) pursuant to the terms of this Agreement. Such additional
sales of Preferred Shares shall be accomplished through execution by such
Purchaser of a signature page to this Agreement and countersignature thereof by
the Company. Photocopies of such additional signature pages shall be delivered
to each other Purchaser. The closing of the purchase and sale of the 


<PAGE>   2
Preferred Shares will be deemed to occur when this Agreement and the other
Transaction Documents (as defined below) have been executed and delivered by
the Company and each Purchaser (which delivery may be effected by facsimile
transmission), and full payment of the Purchase Price has been made by each
Purchaser by wire transfer or immediately available funds against physical
delivery by the Company of duly executed certificates representing the
Preferred Shares purchased by such Purchaser hereunder.

         1.2   Certain Definitions. When used herein, (A) "business day" shall
mean any day on which the New York Stock Exchange and commercial banks in the
city of New York are open for business, (B) an "affiliate" of a party shall mean
any person or entity controlling, controlled by or under common control with
that party and (C) "control" shall mean, with respect to an entity, the ability
to direct the business, operations or management of such entity, whether through
an equity interest therein or otherwise.

2.       REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS.

         Each Purchaser, solely with respect to him or it, hereby makes the
following representations and warranties to the Company and agrees with the
Company that, as of the date of this Agreement:

         2.1   Authorization; Enforceability. If an entity, such Purchaser is 
duly and validly organized, validly existing and in good standing under the laws
of the jurisdiction of its incorporation or organization with full power and
authority to purchase the Preferred Shares and to execute and deliver this
Agreement. This Agreement and the Registration Rights Agreement have been duly
and validly authorized, executed and delivered by or on behalf of such
Purchaser. This Agreement constitutes such Purchaser's valid and legally binding
obligation, enforceable in accordance with its terms.

         2.2   Accredited Investor; Investment Intent. Such Purchaser is an
accredited investor as that term is defined in Rule 501(a) of Regulation D, and
is acquiring the Preferred Shares solely for his or its own account for
investment purposes as a principal and not with a present view to the public
resale or distribution of all or any part thereof, except pursuant to sales that
are exempt from the registration requirements of the Securities Act and/or sales
registered under the Securities Act; provided, however that in making such
representation, such Purchaser does not agree to hold the Securities for any
minimum or specific term and reserves the right to sell, transfer or otherwise
dispose of the Securities at any time in accordance with the provisions of this
Agreement and with Federal and state securities laws applicable to such sale,
transfer or disposition.

         2.3   Information. The Company has provided such Purchaser with
information regarding the business, operations and financial condition of the
Company, and has granted to such Purchaser the opportunity to ask questions of
and receive answers from representatives of the Company, its officers,
directors, employees and agents concerning the Company and materials relating to
the terms and conditions of the purchase and sale of the Preferred Shares
hereunder. Such Purchaser understands that his or its investment in the
Preferred Shares involves a high degree of risk. Such Purchaser has sought such
accounting, legal and tax advice as he or it has considered necessary to make an
informed investment decision with respect to his or its acquisition of the
Preferred Shares.



                                        2
<PAGE>   3

         2.4   Limitations on Disposition. Such Purchaser acknowledges that,
except as provided in the Registration Rights Agreement, the Securities have not
been and are not being registered under the Securities Act and may not be
transferred or resold without registration under the Securities Act or unless
pursuant to an exemption therefrom.

         2.5   Legend. Such Purchaser understands that the certificates
representing the Securities will bear at issuance a restrictive legend in
substantially the following form:

               "The securities represented by this certificate have not been
               registered under the Securities Act of 1933, as amended (the
               "Securities Act"), or the securities laws of any state, and may
               not be offered or sold unless a registration statement under the
               Securities Act and applicable state securities laws shall have
               become effective with regard thereto, or an exemption from
               registration under the Securities Act and applicable state
               securities laws is available in connection with such offer or
               sale. Such securities are issued subject to the provisions of (i)
               the Certificate of Designation relating to the Series A
               Convertible Preferred Stock of Toreador Royalty Corporation (the
               "Company"), (ii) a Securities Purchase Agreement by and among the
               Company and the Purchasers signatory thereto (collectively, the
               "Purchasers") and (iii) a Registration Rights Agreement by and
               among the Company and the Purchasers."

               Notwithstanding the foregoing, it is agreed that, as long as
(A) the resale or transfer (including without limitation a pledge) of any of the
Securities is registered pursuant to an effective registration statement, (B)
such Securities can be sold pursuant to Rule 144 under the Securities Act ("Rule
144") and a registered broker dealer provides to the Company a customary
broker's Rule 144 letter and such Purchaser delivers to the Company a customary
seller's representation letter and a copy of any Form 144 which may have been
required to be filed by such Holder pursuant to Rule 144, or (C) such Securities
are eligible for resale under Rule 144(k), such Securities shall be issued
without any legend or other restrictive language and, with respect to Securities
upon which such legend is stamped, the Company shall issue new certificates
without such legend to the holder upon request.

         2.6   No Governmental Review. Such Buyer understands that no United
States federal or state agency or any other government or governmental agency
has passed on or made any recommendation or endorsement of the Securities or the
fairness or suitability of the investment in the Securities nor have such
authorities passed upon or endorsed the merits of the offering of the
Securities.

         2.7   Residency. Such Purchaser is a resident of that state or
jurisdiction specified on the Purchaser's signature page to this Agreement.

3.       REPRESENTATIONS AND WARRANTIES OF THE COMPANY.

         The Company hereby makes the following representations and warranties
to each Purchaser and agrees with such Purchaser that, as of the date of this
Agreement:

         3.1   Organization, Good Standing and Qualification. Each of the 
Company and its subsidiaries is duly organized, validly existing and in good
standing under the laws of the jurisdiction of its incorporation or organization
and has all requisite corporate power and



                                        3
<PAGE>   4

authority to carry on its business as now conducted. Each of the Company and its
subsidiaries is duly qualified to transact business and is in good standing in
each jurisdiction in which the failure so to qualify would have a material
adverse effect on the consolidated business or financial condition of the
Company and its subsidiaries taken as a whole. The term "subsidiaries" shall
mean entities in which the Company has an equity interest of 50% or greater.

         3.2   Authorization; Consents. The Company has the requisite corporate
power and authority to enter into and perform its obligations under (i) this
Agreement, (ii) the Registration Rights Agreement and (iii) all other
agreements, documents, certificates or other instruments delivered by the
Company contemporaneously herewith (the instruments described in (i), (ii) and
(iii) being collectively referred to herein as the "Transaction Documents"), to
execute and perform its obligations under the Certificate of Designation, to
issue and sell the Preferred Shares to such Purchaser in accordance with the
terms hereof, to issue the Conversion Shares upon conversion of the Preferred
Shares in accordance with the Certificate of Designation, and to issue the
Dividend Payment Shares in accordance with the Certificate of Designation. All
corporate action on the part of the Company by its officers, directors and
stockholders necessary for (A) the authorization, execution and delivery of, and
the performance by the Company of its obligations under, the Transaction
Documents and (B) the authorization, execution and filing of, and the
performance by the Company of its obligations under, the Certificate of
Designation has been taken, and no further consent or authorization of the
Company, its Board of Directors, its stockholders, any governmental agency or
organization (other than such approval as may be required under the Securities
Act and applicable state securities laws in respect of the Registration Rights
Agreement), or any other person or entity is required (pursuant to any rule of
the National Association of Securities Dealers, Inc., other than with respect to
the listing of the Conversion Shares on the Nasdaq National Market System, or
otherwise).

         3.3   Enforcement. The Transaction Documents and the Certificate of
Designation constitute valid and legally binding obligations of the Company,
enforceable in accordance with their respective terms, except as such
enforcement may be limited by (i) applicable bankruptcy, insolvency,
reorganization or other laws of general application relating to or affecting the
enforcement of creditors' rights generally, (ii) general principles of equity
and (iii) as to indemnification under the Securities Act or Exchange Act,
principles of public policy.

         3.4   Disclosure Documents; Agreements; Financial Statements; Other
Information. The Company has filed with the Commission: (i) the Company's Annual
Report on Form 10-K for the year ended December 31, 1997, (ii) Quarterly Reports
on Form 10-Q for the quarters ended March 31, 1998, June 30, 1998 and September
30, 1998, (iii) all Current Reports on Form 8-K required to be filed with the
Commission since December 31, 1997 and (iv) the Company's definitive Proxy
Statement for its 1998 Annual Meeting of Stockholders (collectively, the
"Disclosure Documents"). Each Disclosure Document, as of the date of the filing
thereof with the Commission, conformed in all material respects to the
requirements of the Exchange Act, and the rules and regulations thereunder and,
as of the date of such filing, such Disclosure Document did not contain an
untrue statement of material fact or omit to state a material fact required to
be stated therein or necessary to make the statements therein, in light of the
circumstances under which they were made, not misleading. As of their respective
dates, the financial statements of the Company included in the Disclosure
Documents complied as to form in all material respects with applicable
accounting



                                        4
<PAGE>   5


requirements and the published rules and regulations of the Commission with
respect thereto. Such financial statements have been prepared in accordance with
generally accepted accounting principles consistently applied at the times and
during the periods involved (except (i) as may be otherwise indicated in such
financial statements or the notes thereto, or (ii) in the case of unaudited
interim statements, to the extent they may exclude footnotes or may be condensed
or summary statements) and fairly present in all material respects the financial
position of the Company as of the dates thereof and the results of its
operations and cash flows for the periods then ended (subject, in the case of
unaudited statements, to normal year-end adjustments).

         3.5   Valid Issuance. The Preferred Shares are duly authorized and, 
when issued, sold and delivered in accordance with the terms hereof, (i) will be
duly and validly issued, fully paid and nonassessable, free and clear of any
taxes, liens, claims, preemptive or similar rights or encumbrances imposed by or
through the Company, (ii) based in part upon the representations of such
Purchaser in this Agreement, will be issued, sold and delivered in compliance
with all applicable Federal and state securities laws and (iii) will be entitled
to all of the rights, preferences and privileges set forth in the Certificate of
Designation. The Conversion Shares are duly authorized and reserved for issuance
and, when issued upon conversion of the Preferred Shares in accordance with the
terms of the Certificate of Designation, will be duly and validly issued, fully
paid and nonassessable, free and clear of any taxes, liens, claims, preemptive
or similar rights or encumbrances imposed by or through the Company. The
Dividend Payment Shares are duly authorized and, upon the issuance thereof in
accordance with the terms of the Certificate of Designation, will be duly and
validly issued, fully paid and nonassessable, free and clear of any taxes,
liens, claims, preemptive or similar rights or encumbrances imposed by or
through the Company.

         3.6   No Conflict with Other Instruments. Neither the Company nor any 
of its subsidiaries is in violation of any provisions of its charter, Bylaws or
any other governing document as amended and in effect on and as of the date
hereof or in default (and no event has occurred which, with notice or lapse of
time or both, would constitute a default) under any provision of any instrument
or contract to which it is a party or by which it is bound, or of any provision
of any Federal or state judgment, writ, decree, order, statute, rule or
governmental regulation applicable to the Company, which would have a material
adverse effect on the consolidated business or financial condition of the
Company and its subsidiaries taken as a whole. The (i) execution, delivery and
performance of this Agreement and the other Transaction Documents, (ii)
execution and filing of the Certificate of Designation, and (iii) consummation
of the transactions contemplated hereby and thereby (including without
limitation, the issuance of the Preferred Shares, and the reservation for
issuance and issuance of the Conversion Shares, and the Dividend Payment Shares)
will not result in any such violation or be in conflict with or constitute, with
or without the passage of time and giving of notice, either a default under any
such provision, instrument or contract or an event which results in the creation
of any lien, charge or encumbrance upon any assets of the Company or of any of
its subsidiaries, which violation, conflict, default, lien, charge or
encumbrance would have a material adverse affect on the consolidated business or
financial condition of the Company and its subsidiaries taken as a whole, or the
triggering of any preemptive or anti-dilution rights or rights of first refusal
or first offer on the part of holders of the Company's securities.



                                        5
<PAGE>   6


4.       COVENANTS OF THE COMPANY.

         4.1   Corporate Existence. The Company shall, so long as any Purchaser 
or any affiliate of such Purchaser beneficially owns any Securities, maintain
its corporate existence in good standing and shall pay all taxes owed by it when
due except for taxes which the Company reasonably disputes or as to which the
failure to pay could not reasonably be expected to have a material adverse
effect on the consolidated business or financial condition of the Company and
its subsidiaries taken as a whole.

         4.2   Provision of Information. Upon written request, the Company shall
provide each Purchaser with copies of its annual reports on Form 10-K, quarterly
reports on Form 10-Q, current reports on Form 8-K and proxy statements and other
materials sent to stockholders, in each such case promptly after the filing
thereof with the Commission, until the conversion or redemption of all of the
Preferred Shares held by such Purchaser.

         4.3   Form D; Blue-Sky Qualification. The Company agrees to file a 
Form D with respect to the Securities as required under Regulation D. The
Company shall, on or before the Closing, take such action as is necessary to
qualify the Preferred Shares for sale under applicable state or "blue-sky" laws
or obtain an exemption therefrom.

         4.4   Reporting Status. As long as any Purchaser or any affiliate of 
such Purchaser beneficially owns any Securities and until the date on which any
of the foregoing may be sold to the public pursuant to Rule 144(k) (or any
successor rule or regulation), (i) the Company shall timely file with the
Commission all reports required to be so filed pursuant to the Exchange Act and
(ii) the Company shall not terminate its status as an issuer required by the
Exchange Act to file reports thereunder even if the Exchange Act or the rules or
regulations thereunder would permit such termination.

         4.5   Reservation of Common Stock. The Company shall at all times have
authorized and reserved for issuance, free from any preemptive rights, solely
for the purpose of effecting conversions of the Preferred Shares hereunder, such
number of its shares of Common Stock as shall from time to time be sufficient to
effect the conversion of all of the Preferred Shares in full.

         4.6   Use of Proceeds. The Company shall use the proceeds from the sale
of the Preferred Shares for general corporate purposes only, in the ordinary
course of its business and consistent with past practice and shall not use such
proceeds to make a loan to any employee, officer or director of the Company or
to repurchase or pay a dividend on shares of Common Stock.

         4.7   Quotation on Nasdaq. The Company shall (i) promptly following the
Closing, take such action as may be necessary to include the Conversion Shares
on the Nasdaq National Market System, and (ii) use its best efforts to maintain
the designation and quotation, or listing, of the Common Stock on the Nasdaq
National Market System, the Nasdaq Small Cap Market, the New York Stock Exchange
or the American Stock Exchange.

5.       MISCELLANEOUS.

               5.1    Survival; Severability.  The representations, warranties, 
covenants and indemnities made by the parties herein shall survive the closing 
of this Agreement



                                        6
<PAGE>   7

notwithstanding any due diligence investigation made by or on behalf of the
party seeking to rely thereon, provided that the representations and warranties
contained herein shall survive for two (2) years following the date of this
Agreement. In the event that any provision of this Agreement becomes or is
declared by a court of competent jurisdiction to be illegal, unenforceable or
void, this Agreement shall continue in full force and effect without said
provision; provided that in such case the parties shall negotiate in good faith
to replace such provision with a new provision which is not illegal,
unenforceable or void, as long as such new provision does not materially change
the economic benefits of this Agreement to the parties.

               5.2   Successors and Assigns. The terms and conditions of this
Agreement shall inure to the benefit of and be binding upon the respective
successors and permitted assigns of the parties. Nothing in this Agreement,
express or implied, is intended to confer upon any party other than the parties
hereto or their respective successors and permitted assigns any rights,
remedies, obligations or liabilities under or by reason of this Agreement,
except as expressly provided in this Agreement. The Purchaser may assign its
rights and obligations hereunder, in connection with any private sale or
transfer of the Preferred Shares in accordance with the terms hereof, as long
as, as a condition precedent to such transfer, the transferee executes an
acknowledgment agreeing to be bound by the applicable provisions of this
Agreement, in which case the term "Purchaser" shall be deemed to refer to such
transferee as though such transferee were an original signatory hereto. The
Company may not assign it rights or obligations under this Agreement.

               5.3   Independent Nature of Purchasers' Obligations and Rights.
The obligations of each Purchaser hereunder are several and not joint with the
obligations of the other Purchasers hereunder, and no Purchaser shall be
responsible in any way for the performance of the obligations of any other
Purchaser hereunder. Nothing contained herein or in any other agreement or
document delivered herewith, and no action taken by any Purchaser pursuant
hereto or thereto, shall be deemed to constitute the Purchasers as a
partnership, an association, a joint venture or any other kind of entity, or
create a presumption that the Purchasers are in any way acting in concert with
respect to such obligations or the transactions contemplated by this Agreement.
Each Purchaser shall be entitled to protect and enforce its rights, including
without limitation the rights arising out of the Certificate of Designation,
this Agreement or the other Transaction Documents, and it shall not be necessary
for any other Purchaser to be joined as an additional party in any proceeding
for such purpose.

               5.4   No Reliance; Representations by Purchasers. Each party
acknowledges that (i) it has such knowledge in business and financial matters as
to be fully capable of evaluating this Agreement, the other Transaction
Documents and the transactions contemplated hereby and thereby, (ii) it is not
relying on any advice or representation of the other party in connection with
entering into this Agreement, the other Transaction Documents or such
transactions (other than the representations made in this Agreement or the other
Transaction Documents), (iii) it has not received from such party any assurance
or guarantee as to the merits (whether legal, regulatory, tax, financial or
otherwise) of entering into this Agreement or the other Transaction Documents or
the performance of its obligations hereunder and thereunder, and (iv) it has
consulted with its own legal, regulatory, tax, business, investment, financial
and accounting advisors to the extent that it has deemed necessary, and has
entered into this Agreement and the other Transaction Documents based



                                        7
<PAGE>   8

on its own independent judgment and on the advice of its advisors as it has
deemed necessary, and not on any view (whether written or oral) expressed by
such party.

               5.5   Injunctive Relief. The Company acknowledges that a breach
by it of its obligations hereunder will cause irreparable harm to each Purchaser
and that the remedy or remedies at law for any such breach will be inadequate
and agrees, in the event of any such breach, in addition to all other available
remedies, to an injunction restraining any breach and requiring immediate and
specific performance of such obligations without the necessity of showing
economic loss.

               5.6   Governing Law; Jurisdiction. This Agreement shall be
governed by and construed under the laws of the State of Texas without regard to
the conflict of laws provisions thereof. Each party hereby irrevocably submits
to the non-exclusive jurisdiction of the state and federal courts sitting in the
City of Dallas, Dallas County, for the adjudication of any dispute hereunder or
in connection herewith or with any transaction contemplated hereby or discussed
herein, and hereby irrevocably waives, and agrees not to assert in any suit,
action or proceeding, any claim that it is not personally subject to the
jurisdiction of any such court, that such suit, action or proceeding is brought
in an inconvenient forum or that the venue of such suit, action or proceeding is
improper.

               5.7   Counterparts. This Agreement may be executed in any number
of counterparts, each of which shall be deemed an original, and all of which
together shall constitute one and the same instrument.

               5.8   Headings. The headings used in this Agreement are used for
convenience only and are not to be considered in construing or interpreting this
Agreement.

               5.9   Notices. Any notice, demand or request required or
permitted to be given by any party to any other party pursuant to the terms of
this Agreement shall be in writing and shall be deemed given (i) when delivered
personally or by verifiable facsimile transmission (with an original to follow)
on or before 5:00 p.m., central time, on a business day or, if such day is not a
business day, on the next succeeding business day, (ii) on the next business day
after timely delivery to a nationally-recognized overnight courier and (iii) on
the third business day after deposit in the U.S. mail (certified or registered
mail, return receipt requested, postage prepaid), addressed to the parties as
follows:

               If to the Company:

               Toreador Royalty Corporation
               4809 Cole Avenue
               Suite 108
               Dallas, Texas 75205
               Attn.:  Chief Executive Officer
               Fax:    (214) 369-3183



                                        8
<PAGE>   9

               with a copy to:

               Haynes and Boone, LLP
               901 Main Street, Suite 3100
               Dallas, Texas 75202
               Attn: Janice V. Sharry
               Tel:   214-651-5562
               Fax:   214-651-5940

and if to any Purchaser, to such address for such Purchaser as shall appear on
the signature page hereof executed by such Purchaser, or as shall be designated
by such Purchaser in writing to the Company.

               5.10   Expenses. The Company and each Purchaser shall pay all
costs and expenses that it incurs in connection with the negotiation, execution,
delivery and performance of this Agreement.

               5.11   Entire Agreement; Amendments. This Agreement and the
other Transaction Documents constitute the entire agreement between the parties
with regard to the subject matter hereof and thereof, superseding all prior
agreements or understandings, whether written or oral, between or among the
parties. Except as expressly provided herein, neither this Agreement nor any
term hereof may be amended except pursuant to a written instrument executed by
the Company and the holders of at least two-thirds (2/3) of the Preferred Shares
then outstanding, and no provision hereof may be waived other than by a written
instrument signed by the party against whom enforcement of any such waiver is
sought.


                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]


                                        9
<PAGE>   10

                 SIGNATURE PAGE TO SECURITIES PURCHASE AGREEMENT

         IN WITNESS WHEREOF, the undersigned have executed this Agreement.

PURCHASER NAME:



By:  /s/ WILLIAM I. LEE
     ---------------------------------------   Dated December 7, 1998
     Name: William I. Lee
     Title:


ADDRESS:

         4909 Cole Avenue
         --------------------------------------
         Dallas, Texas 75205
         --------------------------------------


         Tel: 214-521-3222
              ---------------------------------

         Fax: 214-521-8884
              ---------------------------------

Dollar Amount of Series A Preferred Stock to be Purchased:  $ 1,000,000
                                                             ----------------


Accepted this 16th day of December 1998.

TOREADOR ROYALTY CORPORATION



By:  /s/ G. THOMAS GRAVES III
     ---------------------------------------------------
     Name:        G. Thomas Graves III
     Title:       President and Chief Executive Officer



                                       10
<PAGE>   11

                             SCHEDULE OF PURCHASERS

<TABLE>
<CAPTION>
                                                           PURCHASE PRICE OF
PURCHASER NAME                      ADDRESS            SERIES A PREFERRED STOCK
<S>                                <C>                 <C>

</TABLE>





                                       11

<PAGE>   1
                                                                    EXHIBIT 7.11


                          REGISTRATION RIGHTS AGREEMENT


         REGISTRATION RIGHTS AGREEMENT (this "Agreement") by and among Toreador
Royalty Corporation, a Delaware corporation (the "Company"), and each of the
persons listed on the Schedule of Purchasers attached hereto (each referred to
herein as a "Purchaser" and, collectively, as the "Purchasers").

         The Company has agreed, on the terms and subject to the conditions set
forth in the Securities Purchase Agreement of even date herewith (the
"Securities Purchase Agreement"), to issue and sell to each Purchaser shares
(the "Preferred Shares") of the Company's Series A Convertible Preferred Stock,
par value $1.00 per share (the "Preferred Stock"). The Preferred Shares are
convertible pursuant to the Company's Certificate of Designation (the
"Certificate of Designation") into shares (the "Conversion Shares") of the
Company's Common Stock, par value $0.15625 per share (the "Common Stock"). In
order to induce the Purchasers to enter into the Securities Purchase Agreement,
the Company has agreed to provide certain registration rights under the
Securities Act of 1933, as amended (the "Securities Act"), and under applicable
state securities laws. Capitalized terms used herein and not otherwise defined
shall have the respective meanings set forth in the Securities Purchase
Agreement.

         In consideration of each Purchaser entering into the Securities
Purchase Agreement, and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties agree as follows:

1.       DEFINITIONS.

         For purposes of this Agreement, the following terms shall have the
meanings specified:

                  (a) "Closing" shall mean the date hereof;

                  (b) "Demand" means written request to the Company signed by
                  holders of 26% of the Preferred Shares outstanding for the
                  registration of the Conversion Shares;

                  (c) "Registration Deadline" means the one hundred and
                  twentieth (120th) day following a Demand;

                  (d) "Holder" means any person owning or having the right to
                  acquire, through conversion of Preferred Shares, Registrable
                  Securities, including initially each Purchaser and thereafter
                  any permitted assignee thereof;

                  (e) "Register", "registered" and "registration" refer to a
                  registration effected by preparing and filing a registration
                  statement or statements in compliance with the Securities Act
                  and pursuant to Rule 415 under the Securities Act ("Rule 415")
                  or any successor rule providing for the offering of securities
                  on a continuous or delayed basis ("Registration Statement"),
                  and the declaration or ordering of effectiveness of the
                  Registration Statement by the Securities and Exchange
                  Commission (the "Commission"); and
<PAGE>   2
                  (f) "Registrable Securities" means the Conversion Shares, and
                  any other shares of Common Stock issuable pursuant to the
                  terms of the Preferred Stock, whether as a dividend, payment
                  of a redemption price or otherwise, and any shares of capital
                  stock issued or issuable from time to time (with any
                  adjustments) in replacement of, in exchange for or otherwise
                  in respect of the Conversion Shares, including without
                  limitation any securities received by a Holder in connection
                  with an Exchange Transaction (as defined in the Certificate of
                  Designation).

         2.       DEMAND REGISTRATION.

                  (a) On or before the ninetieth (90th) day following a Demand,
the Company shall prepare and file with the Commission a Registration Statement
on Form S-3 (or if the Company is not then eligible to utilize Form S-3 for a
registration of this type, such other form as may be available to the Company)
as a "shelf" registration statement under Rule 415 covering the resale of the
number of shares of Registrable Securities then issuable on conversion of the
Preferred Shares. In addition, the Company may elect to register for resale
shares of Common Stock held by other holders. The Registration Statement shall
state, to the extent permitted by Rule 416 under the Securities Act, that it
also covers such indeterminate number of shares of Common Stock as may be
required to effect conversion of the Preferred Shares to prevent dilution
resulting from stock splits, stock dividends or similar events, or by reason of
changes in the Conversion Price in accordance with the terms of the Certificate
of Designation.

                  (b) The Company shall use its best efforts to cause the
Registration Statement to become effective as soon as practicable following the
filing thereof, but in no event later than the Registration Deadline and shall
maintain the effectiveness of the Registration Statement until the earlier to
occur of (i) the date on which all of the Registrable Securities have been sold
pursuant to the Registration Statement and (ii) the date on which all of the
remaining Registrable Securities (in the reasonable opinion of counsel to the
Company) may be immediately sold to the public without registration and without
regard to the amount of Registrable Securities which may be sold by a Holder
thereof at a given time (the "Registration Period").

                  (c) Upon the declaration by the Commission of the
effectiveness of a Registration Statement with respect to a Demand, the right of
the Holders to make a Demand pursuant to this Section 2 shall terminate and the
Company shall have no further obligation under this Section 2 to file any
additional Registration Statements on Demand. The Company's obligations under
Section 3 shall continue unaffected hereby.

         3.       PIGGYBACK REGISTRATION.

                  If at any time prior to the expiration of the Registration
Period, (i) the Company proposes to register shares of Common Stock under the
Securities Act in connection with the public offering of such shares for cash
(other than a registration relating solely to the sale of securities to
participants in a Company stock plan or employee stock award or a registration
on Form S-4 under the Securities Act or any successor or similar form
registering stock issuable upon a reclassification, a business combination
involving an exchange of securities or an exchange offer for securities of the
issuer or another entity) (a "Proposed Registration") and (ii) a registration
statement covering the sale of all of the Registrable


                                      - 2 -

<PAGE>   3
Securities is not then effective and available for sales thereof by the Holders,
the Company shall, at such time, promptly give each Holder written notice of
such Proposed Registration. Each Holder shall have thirty (30) days from its
receipt of such notice to deliver to the Company a written request specifying
the amount of Registrable Securities that such Holder intends to sell and such
Holder's intended method of distribution. Upon receipt of such request, the
Company shall use its best efforts to cause all Registrable Securities which the
Company has been requested to register to be registered under the Securities Act
to the extent necessary to permit their sale or other disposition in accordance
with the intended methods of distribution specified in the request of such
Holder; provided, however, that the Company shall have the right to postpone or
withdraw any registration effected pursuant to this Section 3 without obligation
to the Holder. If, in connection with any underwritten public offering for the
account of the Company, the managing underwriter(s) thereof shall impose a
limitation on the number of shares of Common Stock which may be included in the
Registration Statement because, in such underwriter(s)' judgment, marketing or
other factors dictate such limitation is necessary to facilitate public
distributions, then the Company shall be obligated to include in such
Registration Statement only such limited portion of the Registrable Securities
with respect to which each Holder has requested inclusion hereunder as such
underwriter(s) shall permit. Any exclusion of Registrable Securities shall be
made pro rata among the Holders seeking to include Registrable Securities in the
Registration Statement, in proportion to the number of Registrable Securities
sought to be included by such Holders; and provided, however, that any exclusion
of Registrable Securities shall be made pro rata with holders of other
securities having the right to include such securities in the Registration
Statement.

         4.       OBLIGATIONS OF THE COMPANY.

         In addition to performing its obligations hereunder, including those
pursuant to Sections 2(a) and 2(b) above, the Company shall:

                  (a) prepare and file with the Commission such amendments and
supplements to the Registration Statement and the prospectus used in connection
with the Registration Statement as may be necessary to comply with the
provisions of the Securities Act or to maintain the effectiveness of the
Registration Statement during the Registration Period, or as may be reasonably
requested by a Holder in order to incorporate information concerning such Holder
or such Holder's intended method of distribution;

                  (b) furnish to each Holder such number of copies of the
prospectus included in such Registration Statement, including a preliminary
prospectus, in conformity with the requirements of the Securities Act, and such
other documents as such Holder may reasonably request in order to facilitate the
disposition of such Holder's Registrable Securities;

                  (c) use all commercially reasonable efforts to register or
qualify the Registrable Securities under the securities or "blue sky" laws of
such jurisdictions within the United States as shall be reasonably requested
from time to time by a Holder, and do any and all other acts or things which may
be necessary or advisable to enable such Holder to consummate the public sale or
other disposition of the Registrable Securities in such jurisdictions; provided
that the Company shall not be required in connection therewith or as a condition
thereto to qualify to do business or to file a general consent to service of
process in any such jurisdiction;


                                      - 3 -

<PAGE>   4
                  (d) in the event of an underwritten public offering of the
Registrable Securities, enter into and perform its obligations under an
underwriting agreement, in usual and customary form reasonably acceptable to the
Company, with the managing underwriter of such offering;

                  (e) notify each Holder immediately upon the occurrence of any
event as a result of which the prospectus included in such Registration
Statement, as then in effect, contains an untrue statement of material fact or
omits to state a material fact required to be stated therein or necessary to
make the statements therein not misleading in light of the circumstances then
existing, and (except during a Blackout Period) as promptly as practicable,
prepare, file and furnish to each Holder a reasonable number of copies of a
supplement or an amendment to such prospectus as may be necessary so that such
prospectus does not contain an untrue statement of material fact or omit to
state a material fact required to be stated therein or necessary to make the
statements therein not misleading in light of the circumstances then existing.
For purposes hereof, "Blackout Period" means such day or days, not to exceed an
aggregate of thirty (30) days during any period of twelve (12) consecutive
months, with respect to which the Board of Directors of the Company determines
in good faith (A) that an amendment or supplement to the Registration Statement
or prospectus contained therein is necessary, in light of subsequent events, in
order to correct a material misstatement made therein or to include information
the absence of which would render the Registration Statement or such prospectus
materially misleading and (B) that the filing of such amendment or supplement
would result in the disclosure of information which the Company has a bona fide
business purpose for preserving as confidential; provided that the Company shall
be entitled to impose no more than three (3) Blackout Periods during any period
of twelve (12) consecutive months;

                  (f) use all commercially reasonable efforts to prevent the
issuance of any stop order or other order suspending the effectiveness of such
Registration Statement and, if such an order is issued, to obtain the withdrawal
thereof at the earliest possible time and to notify each Holder of the issuance
of such order and the resolution thereof;

                  (g) furnish to each Holder, on the date that such Registration
Statement becomes effective, a letter, dated such date, of outside counsel
representing the Company (and reasonably acceptable to such Holder) addressed to
such Holder, confirming the effectiveness of the Registration Statement and, to
the knowledge of such counsel, the absence of any stop order;

                  (h) provide each Holder and its representatives the
opportunity to conduct a reasonable inquiry of the Company's financial and other
records during normal business hours and make available its officers, directors
and employees for questions regarding information which such Holder may
reasonably request in order to fulfill any due diligence obligation on its part;
and

                  (i) permit counsel for each Holder (at such Holder's expense)
to review such Registration Statement and all amendments and supplements thereto
a reasonable period of time prior to the filing thereof with the Commission.


                                      - 4 -

<PAGE>   5
         5.       OBLIGATIONS OF EACH HOLDER.

         In connection with the registration of the Registrable Securities
pursuant to the Registration Statement, each Holder shall:

                  (a) furnish to the Company such information regarding itself
and the intended method of disposition of Registrable Securities as the Company
shall reasonably request in order to effect the registration thereof;

                  (b) upon receipt of any notice from the Company of the
happening of any event of the kind described in Sections 4(e) or 4(f),
immediately discontinue disposition of Registrable Securities pursuant to the
Registration Statement until the filing of an amendment or supplement as
described in Section 4(g) or withdrawal of the stop order referred to in Section
4(f);

                  (c) in the event of an underwritten offering of the
Registrable Securities, enter into a customary and reasonable underwriting
agreement and execute such other documents as the managing underwriter for such
offering may reasonably request;

                  (d) to the extent required by applicable law, deliver a
prospectus to each purchaser of Registrable Securities; and

                  (e) notify the Company when it has sold all of the Registrable
Securities theretofore held by it.

         6.       INDEMNIFICATION.

         In the event that any Registrable Securities are included in a
Registration Statement under this Agreement:

                  (a) To the extent permitted by law, the Company shall
indemnify and hold harmless each Holder, the officers, directors, employees,
agents and representatives of such Holder, and each person, if any, who controls
such Holder within the meaning of the Securities Act or the Securities Exchange
Act of 1934, as amended (the "1934 Act"), against any losses, claims, damages,
liabilities or reasonable out-of-pocket expenses (whether joint or several)
(collectively, including legal or other expenses reasonably incurred in
connection with investigating or defending same, "Losses"), insofar as any such
Losses arise out of or are based upon (i) any untrue statement or alleged untrue
statement of a material fact contained in such Registration Statement, including
any preliminary prospectus or final prospectus contained therein or any
amendments or supplements thereto, or (ii) the omission or alleged omission to
state therein a material fact required to be stated therein, or necessary to
make the statements therein, in light of the circumstances under which they were
made, not misleading. The Company will reimburse such Holder, and each such
officer, director, employee, agent, representative or controlling person for any
legal or other expenses as reasonably incurred by any such entity or person in
connection with investigating or defending any Loss; provided, however, that the
foregoing indemnity shall not apply to amounts paid in settlement of any Loss if
such settlement is effected without the consent of the Company (which consent
shall not be unreasonably withheld), nor shall the Company be obligated to
indemnify any person for any Loss to the extent that such Loss arises out of or
is based upon and in conformity with written information furnished by such
person expressly


                                      - 5 -

<PAGE>   6
for use in such Registration Statement; and provided, further, that the Company
shall not be required to indemnify any person to the extent that any Loss
results from such person selling Registrable Securities (i) to a person to whom
there was not sent or given, at or prior to the written confirmation of the sale
of such shares, a copy of the prospectus, as most recently amended or
supplemented, if the Company has previously furnished or made available copies
thereof or (ii) during any period following written notice by the Company to
such Holder of an event described in Section 4(e) or 4(f).

                  (b) To the extent permitted by law, each Holder, acting
severally and not jointly, shall indemnify and hold harmless the Company, the
officers, directors, employees, agents and representatives of the Company, and
each person, if any, who controls the Company within the meaning of the
Securities Act or the 1934 Act, against any Losses to the extent (and only to
the extent) that any such Losses arise out of or are based upon and in
conformity with written information furnished by such Holder expressly for use
in such Registration Statement; and such Holder will reimburse any legal or
other expenses as reasonably incurred by the Company and any such officer,
director, employee, agent, representative, or controlling person, in connection
with investigating or defending any such Loss; provided, however, that the
foregoing indemnity shall not apply to amounts paid in settlement of any such
Loss if such settlement is effected without the consent of such Holder, which
consent shall not be unreasonably withheld; provided, that, in no event shall
any indemnity under this Section 6(b) exceed the net purchase price of
securities sold by such Holder under the Registration Statement.

                  (c) Promptly after receipt by an indemnified party under this
Section 6 of notice of the commencement of any action (including any
governmental action), such indemnified party will, if a claim in respect thereof
is to be made against any indemnifying party under this Section 6, deliver to
the indemnifying party a written notice of the commencement thereof and the
indemnifying party shall have the right to participate in and to assume the
defense thereof with counsel mutually satisfactory to the parties; provided,
however, that an indemnified party shall have the right to retain its own
counsel, with the reasonably incurred fees and expenses of one such counsel to
be paid by the indemnifying party, if representation of such indemnified party
by the counsel retained by the indemnifying party would be inappropriate under
applicable standards of professional conduct due to actual or potential
conflicting interests between such indemnified party and any other party
represented by such counsel in such proceeding. The failure to deliver written
notice to the indemnifying party within a reasonable time of the commencement of
any such action, to the extent prejudicial to its ability to defend such action,
shall relieve such indemnifying party of any liability to the indemnified party
under this Section 6 with respect to such action, but the omission so to deliver
written notice to the indemnifying party will not relieve it of any liability
that it may have to any indemnified party otherwise than under this Section 6 or
with respect to any other action.

                  (d) In the event that the indemnity provided in subsection (a)
or (b) of this Section 6 is unavailable or insufficient to hold harmless an
indemnified party for any reason, the Company and each Holder agree, severally
and not jointly, to contribute to the aggregate Losses to which the Company or
such Holder may be subject in such proportion as is appropriate to reflect the
relative fault of the Company and such Holder in connection with the statements
or omissions which resulted in such Losses; provided, however, that in no case
shall such Holder be responsible for any amount in excess of the net purchase
price of securities sold by it under the Registration Statement. Relative fault
shall be determined by


                                      - 6 -

<PAGE>   7
reference to whether any alleged untrue statement or omission relates to
information provided by the Company or by such Holder. The Company and each
Holder agree that it would not be just and equitable if contribution were
determined by pro rata allocation or any other method of allocation which does
not take account of the equitable considerations referred to above.
Notwithstanding the provisions of this paragraph (d), no person guilty of
fraudulent misrepresentation (within the meaning of Section 11(f) of the
Securities Act) shall be entitled to contribution from any person who is not
guilty of such fraudulent misrepresentation. For purposes of this Section 6,
each person who controls a Holder within the meaning of either the Securities
Act or the Exchange Act and each officer, director, employee, agent or
representative of such Holder shall have the same rights to contribution as such
Holder, and each person who controls the Company within the meaning of either
the Securities Act or the Exchange Act and each officer, director, employee,
agent or representative of the Company shall have the same rights to
contribution as the Company, subject in each case to the applicable terms and
conditions of this subsection (d).

                  (e) The obligations of the Company and each Holder under this
Section 6 shall survive the conversion or redemption, if any, of the Preferred
Shares, the exercise of the Warrant, the completion of any offering of
Registrable Securities pursuant to a Registration Statement under this
Agreement, or otherwise.

         7.       REPORTS.

                  With a view to making available to each Holder the benefits of
Rule 144 under the Securities Act ("Rule 144") and any other similar rule or
regulation of the Commission that may at any time permit such Holder to sell
securities of the Company to the public without registration, the Company agrees
to:

                  (a) make and keep public information available, as those terms
are understood and defined in Rule 144;

                  (b) file with the Commission in a timely manner all reports
and other documents required of the Company under the Securities Act and the
1934 Act; and

                  (c) furnish to such Holder, so long as such Holder owns any
Registrable Securities, forthwith upon request (i) a written statement by the
Company, if true, that it has complied with the reporting requirements of Rule
144, the Securities Act and the 1934 Act, (ii) a copy of the most recent annual
or quarterly report of the Company and such other reports and documents so filed
by the Company, and (iii) such other information as may be reasonably requested
in availing such Holder of any rule or regulation of the Commission which
permits the selling of any such securities without registration.

         8.       MISCELLANEOUS.

                  (a) Expenses of Registration. All expenses, other than
underwriting discounts and commissions and fees and expenses of counsel to each
Holder, incurred in connection with the registrations, filings or qualifications
described herein, including (without limitation) all registration, filing and
qualification fees, printers' and accounting fees and the fees and disbursements
of counsel for the Company shall be borne by the Company.


                                      - 7 -

<PAGE>   8
                  (b) Amendment; Waiver. Any provision of this Agreement may be
amended only pursuant to a written instrument executed by the Company and
Holders of at least two thirds (2/3) of the Registrable Securities then issued
or issuable. Any waiver of the provisions of this Agreement may be made only
pursuant to a written instrument executed by the party against whom enforcement
is sought. Any amendment or waiver effected in accordance with this paragraph
shall be binding upon each Holder, each future Holder, and the Company. The
failure of any party to exercise any right or remedy under this Agreement or
otherwise, or the delay by any party in exercising such right or remedy, shall
not operate as a waiver thereof. Provided, however, that upon the issuance of
additional shares of Series A Preferred Stock subsequent to the date hereof and
in accordance with the Securities Purchase Agreement, without any further
consent or acknowledgment of the Holders party hereto, the Company may add
additional holders of Series A Preferred Stock to this Agreement from time to
time. Any such additional holders joining this Agreement shall execute a
signature page to this Agreement, which signature page shall be countersigned by
the Company and the original appended to this Agreement. A photocopy of such
appended signature page shall be sent to each prior Holder party to this
Agreement.

                  (c) Notices. Any notice, demand or request required or
permitted to be given by any party to any other party pursuant to the terms of
this Agreement shall be in writing and shall be deemed given (i) when delivered
personally or by verifiable facsimile transmission (with an original to follow)
on or before 5:00 p.m., central time, on a business day or, if such day is not a
business day, on the next succeeding business day, (ii) on the next business day
after timely delivery to a nationally-recognized overnight courier and (iii) on
the third business day after deposit in the U.S. mail (certified or registered
mail, return receipt requested, postage prepaid), addressed to the parties as
follows:

                  If to the Company:

                  Toreador Royalty Corporation
                  4809 Cole Avenue
                  Suite 108
                  Dallas, Texas  75205
                  Attn.: Chief Executive Officer
                  Fax:   214-369-3183

                  with a copy to:

                  Haynes and Boone, LLP
                  901 Main Street, Suite 3100
                  Dallas, Texas 75202
                  Attn.: Janice V. Sharry
                  Tel:   214-651-5562
                  Fax:   214-651-5940

and if to any Holder, to such address as shall be designated by such Holder in
writing to the Company.

                  (d) Termination. This Agreement shall terminate on the earlier
to occur of (a) the end of the Registration Period and (b) the date on which all
of the Registrable Securities have been publicly distributed; but any such
termination shall be without prejudice


                                      - 8 -

<PAGE>   9
to (i) the parties' rights and obligations arising from breaches of this
Agreement occurring prior to such termination and (ii) the indemnification and
contribution obligations under this Agreement.

                  (e) Assignment. The rights of a Holder hereunder shall be
assigned automatically to any transferee of the Preferred Shares or Registrable
Securities from such Holder as long as: (i) the Company is, within a reasonable
period of time following such transfer, furnished with written notice of the
name and address of such transferee, (ii) the transferee agrees in writing with
the Company to be bound by all of the provisions hereof and (iii) such transfer
is made in accordance with the applicable requirements of the Securities
Purchase Agreement.

                  (f) Counterparts. This Agreement may be executed in two or
more counterparts, each of which shall be deemed an original, and all of which
together shall be deemed one and the same instrument. This Agreement, once
executed by a party, may be delivered to any other party hereto by facsimile
transmission.

                  (g) Governing Law. This Agreement shall be governed by and
construed in accordance with the laws of the State of Texas without regard to
the conflict of laws provisions thereof.


                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]


                                      - 9 -

<PAGE>   10
                 SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT

         IN WITNESS WHEREOF, the undersigned have executed this Agreement as of
the date indicated by their signature.


PURCHASER NAME: William I. Lee                        Dated:  December 7, 1998
                ----------------------------------                      


By: /s/ WILLIAM I. LEE
    ----------------------------------------------------
    Name: William I. Lee   
    Title:   
    Address: 4809 Cole Avenue
             Dallas, Texas 75205
    Facsimile: 214-521-8884



Accepted this 16th day of December 1998.

TOREADOR ROYALTY CORPORATION



By: /s/ G. THOMAS GRAVES III
    ----------------------------------------------------
    Name:  G. Thomas Graves III
    Title: President and Chief Executive Officer


                                     - 10 -

<PAGE>   1
                                                                    EXHIBIT 7.12


                           CERTIFICATE OF DESIGNATION

                                       OF

                      SERIES A CONVERTIBLE PREFERRED STOCK

                                       OF

                          TOREADOR ROYALTY CORPORATION


                         Pursuant to Section 151 of the
                        Delaware General Corporation Law


         Toreador Royalty Corporation, a corporation organized and existing
under the laws of the State of Delaware (the "Corporation"), hereby certifies
that the following resolutions were adopted by the Board of Directors of the
Corporation pursuant to authority of the Board of Directors as required by
Section 151 of the Delaware General Corporation Law.

         RESOLVED, that pursuant to the authority granted to the Board of
Directors in accordance with the provisions of the Corporation's Restated
Certificate of Incorporation, the Board of Directors hereby authorizes a series
of the Corporation's previously authorized Preferred Stock, par value $1.00 per
share (the "Preferred Stock"), and hereby states the designation and number of
shares, and fixes the relative rights, preferences, privileges and restrictions
thereof as follows:

1.       DESIGNATION AND AMOUNT.

         The designation of this series, which consists of 160,000 shares (each
such share being referred to herein as a "Preferred Share" and all such shares
being collectively referred to as the "Preferred Shares") of Preferred Stock, is
the Series A Convertible Preferred Stock (the "Series A Preferred Stock") and
the face amount shall be Twenty-Five Dollars ($25.00) per share (the "Stated
Value"). The Preferred Shares will be issued pursuant to the provisions of a
Securities Purchase Agreement by and among the Corporation and the purchasers
named therein (the "Securities Purchase Agreement").

2.       DIVIDENDS.

         (a) Dividend Rate; Payments. The holders (each, a "Holder" and
collectively, the "Holders") of Preferred Shares shall be entitled to receive,
to the extent permitted by applicable law, in preference to the payment of any
dividend on any class or series of Junior Securities (as defined below),
cumulative dividends ("Dividends") on each Preferred Share in an amount equal
to, on an annualized basis, the Stated Value of such Preferred Share times nine
percent (9%). Dividends shall accrue and cumulate on each Preferred Share from
the date of the original issuance thereof (the "Purchase Date") through the
earlier to occur of (A) the payment thereof in accordance with the terms of this
Section 2(a) and (B) the redemption or conversion of such Preferred Share in
accordance with the terms hereof. At the option of the Corporation, Dividends
may be paid in cash or may be paid, in whole or in part, by issuing additional
fully paid and nonassessable shares (the "Dividend Payment Shares") of Preferred
Stock. Accrued Dividends on each outstanding Preferred Share shall be payable

<PAGE>   2




in four quarterly installments on the last day of March, June, September and
December of each year commencing March 31, 1999 unless earlier due and payable
on a Conversion Date (as defined below) or a Redemption Date (as defined below)
(each, a "Dividend Payment Date"). If, on any date, Dividends on any outstanding
Preferred Shares have not been paid or declared by the Board of Directors in
accordance with applicable law and set aside for payment with respect to all
Dividend Payment Dates preceding such date, the aggregate amount of such
Dividends shall be fully paid or declared and set aside for payment before any
distribution, whether by way of dividend or otherwise, shall be declared, paid
or set apart with respect to any Junior Securities on or after such date.

         (b) Delivery of Dividends. The Corporation shall mail any cash
dividends declared by check to the Holder or its nominee postmarked no later
than three (3) Business Days (as defined below) following the applicable
Dividend Payment Date. If the Corporation declares any dividends payable in
Preferred Stock, the Corporation shall deliver to each Holder, on or before the
third (3rd) Business Day following the applicable Dividend Payment Date (the
"Dividend Payment Share Delivery Date"), the aggregate number of whole Dividend
Payment Shares that is determined by dividing (x) the amount of the Dividend to
which such Holder is entitled as of such Dividend Payment Date with respect to
all of such Holder's Preferred Shares by (y) the Stated Value. The Corporation
shall effect delivery of Dividend Payment Shares by delivering to the Holder or
its nominee physical certificates representing such Dividend Payment Shares, no
later than the close of business on such Dividend Payment Share Delivery Date.
No fractional Dividend Payment Shares shall be issued; the Corporation shall, in
lieu thereof, at its sole discretion, either issue a number of Dividend Payment
Shares which reflects a rounding up to the next whole number of shares or pay
cash in an amount calculated by multiplying the amount of the fractional share
times the Stated Value. Dividend Payment Shares shall be fully paid and
non-assessable, free and clear of any liens, claims, preemptive rights or
encumbrances imposed by or through the Corporation (other than restrictions on
transfer required under applicable securities laws).

3.       PRIORITY.

         (a)      Payment upon Dissolution.

                  (i) Upon the occurrence of (x) any insolvency or bankruptcy
proceedings, or any receivership, liquidation, reorganization or other similar
proceedings in connection therewith, commenced by the Corporation or by its
creditors, as such, or relating to its assets or (y) the dissolution or other
winding up of the Corporation whether total or partial, whether voluntary or
involuntary and whether or not involving insolvency or bankruptcy proceedings,
or (z) any assignment for the benefit of creditors or any marshalling of the
material assets or material liabilities of the Corporation (each, a "Liquidation
Event"), no distribution shall be made to the holders of any shares of Junior
Securities (as defined below) unless each Holder shall have received the
Liquidation Preference (as defined below) with respect to each Preferred Share
then held by such Holder. In the event that upon the occurrence of a Liquidation
Event the assets available for distribution to the Holders are insufficient to
pay the Liquidation Preference (as defined below) with respect to all of the
outstanding Preferred Shares and the preferential amounts payable to such
holders, the entire assets of the Corporation shall be distributed ratably among
the outstanding Preferred Shares in proportion to the ratio that the
preferential amount payable on each such share (which shall be the Liquidation
Preference in the case of a Preferred Share) bears to the aggregate preferential
amount payable on all such shares.



                                      -2-
<PAGE>   3





                  (ii) The "Liquidation Preference" with respect to a Preferred
Share shall mean an amount equal to the Stated Value of such Preferred Share
(subject to ratable adjustment in the event of any stock split or combination of
the Series A Preferred Stock and to equitable adjustment in the event of a
reclassification of the Series A Preferred Stock or other similar event) plus
any accrued and unpaid Dividends thereon. "Junior Securities" shall mean the
Common Stock and all other capital stock of the Corporation.

4.       CONVERSION.

         (a) Right to Convert. Each Holder shall have the right to convert, at
any time and from time to time from and after the Purchase Date, all or any part
of the Preferred Shares held by such Holder, unless previously redeemed, into
such number of fully paid and non-assessable shares of Common Stock ("Conversion
Shares") as is computed in accordance with the terms hereof (a "Conversion").

         (b) Conversion Notice. In order to convert Preferred Shares, a Holder
shall send by facsimile transmission, at any time prior to 5:00 p.m., central
time, on the date on which such Holder wishes to effect such Conversion (the
"Conversion Date"), (i) a notice of conversion (a "Conversion Notice"), in
substantially the form of Exhibit A hereto, to the Corporation and to its
designated transfer agent for the Common Stock (the "Transfer Agent") stating
the number of Preferred Shares to be converted, the applicable Conversion Price
(as defined below) and a calculation of the number of shares of Common Stock
issuable upon such Conversion and (ii) a copy of the certificate or certificates
representing the Preferred Shares being converted. The Holder shall thereafter
send the original of the Conversion Notice and of such certificate or
certificates to the Transfer Agent. The Corporation shall issue a new
certificate for Preferred Shares in the event that less than all of the
Preferred Shares represented by a certificate delivered to the Corporation in
connection with a Conversion are converted. Except as otherwise provided herein,
upon delivery of a Conversion Notice by a Holder in accordance with the terms
hereof, such Holder shall, as of the applicable Conversion Date, be deemed for
all purposes to be record owner of the Common Stock to which such Conversion
Notice relates. In the case of a dispute between the Corporation and a Holder as
to the calculation of the Conversion Price or the number of Conversion Shares or
Dividend Payment Shares issuable upon a Conversion, the Corporation shall
promptly issue to such Holder the number of Conversion Shares and Dividend
Payment Shares that are not disputed and shall submit the disputed calculations
to the Corporation's independent accountant within three (3) Business Days of
receipt of such Holder's Conversion Notice. The Corporation shall cause such
accountant to calculate the Conversion Price as provided herein and to notify
the Corporation and such Holder of the results in writing no later than three
(3) Business Days following the day on which it received the disputed
calculations. The Corporation shall deliver the Conversion Shares and Dividend
Payment Shares, if any, owed to a Holder pursuant to such accountant's
calculations on or before the close of business on the third (3rd) Business Day
following the Corporation's receipt of notice from such accountant of the
results of its calculations. Such accountant's calculation shall be deemed
conclusive absent manifest error. The fees of any such accountant shall be borne
by the party whose calculations were most at variance with those of such
accountant.

         (c) Number of Conversion Shares; Conversion Price. The number of
Conversion Shares to be delivered by the Corporation pursuant to a Conversion
shall be determined by dividing the aggregate Stated Value of the Preferred
Shares to be converted by the Conversion Price (as defined herein) in effect on
the applicable Conversion Date. Subject to 



                                      -3-
<PAGE>   4



adjustment as provided in Section 5 below, "Conversion Price" shall mean Four
Dollars ($4.00).

         (d) Certain Definitions. "Trading Day" shall mean any day on which the
Common Stock is traded on the Nasdaq National Market System or on the principal
securities exchange or market located in the United States on which the Common
Stock is then traded. "Business Day" means any day on which the New York Stock
Exchange and commercial banks located in the City of New York are open for
business.

         (e) Delivery of Common Stock Upon Conversion. Upon receipt of a
Conversion Notice from a Holder pursuant to paragraph 4(b) above, the
Corporation shall, no later than the close of business on (A) the later to occur
of (i) the third (3rd) Business Day following the Conversion Date set forth in
such Conversion Notice and (ii) the first Business Day following delivery of the
original certificates, duly endorsed, representing the Preferred Shares being
converted pursuant thereto and (B) with respect to Conversion Shares which are
disputed as described in paragraph 4(b) above, and required to be delivered by
the Corporation pursuant to the accountant's calculations described therein, the
date for delivery thereof specified in such paragraph 4(b) (the "Delivery
Date"), issue and deliver or cause to be delivered to such Holder the number of
Conversion Shares as shall be determined as provided herein. The Corporation
shall effect delivery of Conversion Shares by delivering to the Holder or its
nominee physical certificates representing such Conversion Shares, no later than
the close of business on such Delivery Date. If any Conversion would create a
fractional Conversion Share, such fractional Conversion Share shall be
disregarded and, at the Corporation's sole discretion, either the number of
Conversion Shares issuable upon such Conversion, in the aggregate, shall be the
next higher number of Conversion Shares or the Corporation shall pay cash in an
amount calculated by multiplying the amount of the fractional share times the
Conversion Price for such Conversion.

5.       ADJUSTMENTS TO CONVERSION PRICE.

         (a) Adjustment to Conversion Price Due to Stock Split, Stock Dividend,
Etc. If, prior to the Conversion of all of the Preferred Shares, (A) the number
of outstanding shares of Common Stock is increased by a stock split, a stock
dividend on the Common Stock, a reclassification of the Common Stock, the
distribution to holders of Common Stock as a class of rights or warrants
entitling them to subscribe for or purchase Common Stock at less than the then
current market price thereof (based upon the subscription or exercise price of
such rights or warrants at the time of the issuance thereof) or other similar
event, the Conversion Price shall be proportionately reduced, or (B) the number
of outstanding shares of Common Stock is decreased by a reverse stock split,
combination or reclassification of shares or other similar event, the Conversion
Price shall be proportionately increased. In such event, the Corporation shall
notify the Transfer Agent of such change on or before the effective date
thereof.

         (b) Adjustment Due to Merger, Consolidation, Etc. If, prior to the
Conversion of all of the Preferred Shares, there shall be any merger,
consolidation, business combination, tender offer, exchange of shares,
recapitalization, reorganization, redemption or other similar event, as a result
of which shares of Common Stock shall be exchanged for or changed into the same
or a different number of shares of the same or another class or classes of stock
or securities of the Corporation or another entity (an "Exchange Transaction"),
then such Holder shall (A) upon the consummation of such Exchange Transaction,
have the right to receive,



                                      -4-
<PAGE>   5




with respect to any shares of Common Stock then held by such Holder, or which
such Holder is then entitled to receive pursuant to a Conversion Notice
previously delivered by such Holder, (and without regard to whether such shares
contain a restrictive legend or are freely-tradeable) the same amount and type
of consideration (including without limitation, stock, securities and/or other
assets) and on the same terms as a holder of shares of Common Stock would be
entitled to receive in connection with the consummation of such Exchange
Transaction (the "Exchange Consideration"), and (B) upon the Conversion of
Preferred Shares occurring subsequent to the consummation of such Exchange
Transaction, the Exchange Consideration which such Holder would have been
entitled to receive in connection with such Exchange Transaction had such shares
been converted immediately prior to such Exchange Transaction, and in any such
case appropriate provisions shall be made with respect to the rights and
interests of such Holder to the end that the provisions hereof (including,
without limitation, provisions for the adjustment of the Conversion Price and of
the number of shares issuable upon a Conversion) shall thereafter be applicable
as nearly as may be practicable in relation to any securities thereafter
deliverable upon the Conversion of such Preferred Shares. The Corporation shall
not effect any Exchange Transaction unless (i) it first gives to each Holder
twenty (20) days prior written notice of such Exchange Transaction (an "Exchange
Notice"), and makes a public announcement of such event at the same time that it
gives such notice and (ii) the resulting successor or acquiring entity (if not
the Corporation) assumes by written instrument the obligations of the
Corporation hereunder, including the terms of this subparagraph 6(b), and under
the Securities Purchase Agreement and the Registration Rights Agreement
described in the Securities Purchase Agreement (the "Registration Rights
Agreement").

         (c) Distribution of Assets. If the Corporation shall declare or make
any distribution of cash, evidences of indebtedness or other securities or
assets (other than cash dividends or distributions payable out of earned surplus
or net profits for the current or the immediately preceding year), or any rights
to acquire any of the foregoing, to holders of Common Stock as a partial
liquidating dividend, by way of return of capital or otherwise, including any
dividend or distribution in shares of capital stock of a subsidiary of the
Corporation (collectively, a "Distribution"), then, upon a Conversion by a
Holder occurring after the record date for determining stockholders entitled to
such Distribution, the Conversion Price for Preferred Shares not converted prior
to the record date of a Distribution shall be reduced to a price determined by
decreasing the Conversion Price in effect immediately prior to the record date
of the Distribution by an amount equal to the fair market value of the assets so
distributed with respect to each share of Common Stock, such fair market value
to be determined by an investment banking firm selected by the Corporation.

         (d) No Fractional Shares. If any adjustment under this Section would
create a fractional share of Common Stock or a right to acquire a fractional
share of Common Stock, such fractional share shall be disregarded and, at the
Corporation's sole discretion, either the number of shares of Common Stock
issuable upon Conversion shall be the next higher number of shares or the
Corporation shall pay in cash an amount calculated by multiplying the amount of
the fractional share times the Conversion Price for such Conversion.



                                      -5-
<PAGE>   6





6.       OPTIONAL REDEMPTION BY CORPORATION.

         (a) Optional Redemption. Any time on or after December 1, 2001, the
Corporation shall have the right to redeem, in while or in part, Preferred
Shares outstanding at the Optional Redemption Price (as defined below) (an
"Optional Redemption"), to the extent permitted by applicable law and so long as
(A) the Corporation shall have sufficient cash available on the Optional
Redemption Date to effect such Optional Redemption and (B) the Corporation shall
have delivered to each Holder at least fifteen (15) Trading Days' prior written
notice (an "Optional Redemption Notice") specifying the date on which such
Optional Redemption is to be effected (the "Optional Redemption Date") and the
amount of the Optional Redemption Price payable to such Holder. If the
Corporation should elect to redeem less than all of the Preferred Shares
outstanding, the Corporation shall select those Preferred Shares to be redeemed
by lot. Nothing contained herein shall limit a Holder's right to convert its
Preferred Shares at any time prior to the Optional Redemption Date.

         (b) Optional Redemption Price. The "Optional Redemption Price" to be
paid by the Corporation to a Holder in the event of an Optional Redemption shall
be equal to the Liquidation Preference of the Preferred Shares then held by such
Holder multiplied by (i) 1.03 if the Optional Redemption Date is on or after
December 1, 2001 but before December 1, 2002, (ii) 1.02 if the Optional
Redemption Date is on or after December 1, 2002 and before December 1, 2003,
(iii) 1.01 if the Optional Redemption Date is on or after December 1, 2003 and
before December 1, 2004, or (iv) 1.00 if the Optional Redemption Date is on or
after December 1, 2004, plus in all cases, accrued and unpaid Dividends through
and including the Optional Redemption Date.

         (c) Payment of Optional Redemption Price. Upon the redemption of a
Preferred Share, payment of the Optional Redemption Price, which shall be in the
form of a Corporation check, to the Holder thereof will be effected
simultaneously with the return of such share by such Holder to the Corporation.
To the extent the Corporation shall redeem less than all of the Preferred Shares
outstanding, the Corporation shall also deliver certificates evidencing the
unredeemed Preferred Shares in addition to the Optional Redemption Price.

7.       MANDATORY REDEMPTION BY THE CORPORATION.

         (a) Mandatory Redemption. On December 1, 2008, the Corporation shall
redeem, in whole or in part, Preferred Shares outstanding in same day funds at
the Mandatory Redemption Price (as defined below) (a "Mandatory Redemption"), to
the extent permitted by applicable law and so long as the Corporation shall have
delivered to each Holder at least fifteen (15) Trading Days' prior written
notice (a "Mandatory Redemption Notice") specifying the date on which such
Mandatory Redemption is to be effected (the "Mandatory Redemption Date") and the
amount of the Mandatory Redemption Price payable to such Holder. Nothing
contained herein shall limit a Holder's right to convert its Preferred Shares at
any time prior to the Mandatory Redemption Date.

         (b) Mandatory Redemption Price. The "Mandatory Redemption Price" shall
be equal to the Liquidation Preference of the Preferred Shares being redeemed.


                                      -6-
<PAGE>   7




         (c) Payment of Mandatory Redemption Price. Upon the redemption of a
Preferred Share, payment of the Mandatory Redemption Price, which shall be in
the form of a Corporation check, to the Holder thereof will be effected
simultaneously with the return of such share by such Holder to the Corporation.

8.       MISCELLANEOUS.

         (a) Transfer of Preferred Shares. A Holder may sell or transfer all or
any portion of the Preferred Shares to any person or entity as long as such sale
or transfer is the subject of an effective registration statement under the
Securities Act or is exempt from registration thereunder and otherwise is made
in accordance with the terms of the Securities Purchase Agreement. From and
after the date of such sale or transfer, the transferee thereof shall be deemed
to be a Holder. Upon any such sale or transfer, the Corporation shall, promptly
following the return of the certificate or certificates representing the
Preferred Shares that are the subject of such sale or transfer, issue and
deliver to such transferee a new certificate in the name of such transferee.

         (b) Notices. Except as otherwise provided herein, any notice, demand or
request required or permitted to be given pursuant to the terms hereof, the form
or delivery of which notice, demand or request is not otherwise specified
herein, shall be in writing and shall be deemed given (i) when delivered
personally or by verifiable facsimile transmission on or before 5:00 p.m.,
central time, on a Business Day or, if such day is not a Business Day, on the
next succeeding Business Day, (ii) on the next Business Day after timely
delivery to an overnight courier and (iii) on the third Business Day after
deposit in the U.S. mail (certified or registered mail, return receipt
requested, postage prepaid), addressed to the parties as follows:

                  If to the Corporation:

                  Toreador Royalty Corporation
                  4809 Cole Avenue
                  Suite 108
                  Dallas, Texas 75205

                  Attn.:   Chief Executive Officer
                  Fax:     214-369-3183

and if to any Holder, to such address for such Holder as shall be designated by
such Holder in writing to the Corporation.

         (c) Lost or Stolen Certificate. Upon receipt by the Corporation of
evidence of the loss, theft, destruction or mutilation of a certificate
representing Preferred Shares, and (in the case of loss, theft or destruction)
of indemnity or security reasonably satisfactory to the Corporation, and upon
surrender and cancellation of such certificate if mutilated, the Corporation
shall execute and deliver to the Holder a new certificate identical in all
respects to the original certificate.

         (d) No Voting Rights. Except as provided by applicable law and
paragraph 8(e) below, the Holders of the Preferred Shares shall have no voting
rights with respect to the business, management or affairs of the Corporation.
The Corporation shall provide each 



                                      -7-
<PAGE>   8



Holder with prior notification of each meeting of stockholders (and copies of
proxy statements and other information sent to such stockholders).

         (e)      Protective Provisions.

                  (A) So long as shares of Series A Preferred Stock are
outstanding, the Corporation shall not, without first obtaining the approval of
the Holders of at a majority of the then outstanding shares of Series A
Preferred Stock:

                           (i) alter or change the rights, preferences or
privileges of the Series A Preferred Stock or any other capital stock of the
Corporation so as to affect adversely the Series A Preferred Stock;

                           (ii) create any new class or series of capital stock
having a preference over or ranking pari passu with the Series A Preferred Stock
as to redemption, the payment of dividends or distribution of assets upon a
Liquidation Event or any other liquidation, dissolution or winding up of the
Corporation;

                           (iii) increase the authorized number of shares of
Preferred Stock;

                           (iv) re-issue any shares of Series A Preferred Stock
which have been converted in accordance with the terms hereof; or

                           (v) declare, pay or make any provision for any cash
dividend or distribution with respect to the Common Stock of the Corporation.

                  (B) If the Corporation (i) fails to pay dividends in respect
of four quarterly dividend periods, or (ii) fails to make a Mandatory
Redemption, holders of a majority of the outstanding shares of the Preferred
Stock would be entitled acting separately as a class, to elect one person to the
Board of Directors of the Corporation. Upon the taking of such action, the
maximum authorized number of members of the Board of Directors shall
automatically increase by one person so elected, and the vacancy so created
shall be filled by the person elected pursuant to this subparagraph (B). A
director elected by the holders of Series A Preferred Stock pursuant to this
subparagraph (B) shall serve until his successor is duly elected and qualified,
until his removal or until his term terminates as provided below. Such a
director may be removed without cause at any time by action, and only by such
action, of the holders of shares of Series A Preferred Stock. If the office of a
director elected pursuant to this subparagraph (B) becomes vacant by reason of
death, resignation, retirement, disqualification, removal from office or
otherwise, such vacancy may be filled by the action, and only by such action, of
the holders of shares of Series A Preferred Stock. At such time as the event of
default giving rise to this right to elect a director has been cured, such right
shall terminate, the term of any director elected pursuant to this subparagraph
(B) shall terminate and the maximum number of authorized members of the Board of
Directors shall decrease automatically to the maximum number of authorized
members of the Board of Directors in effect immediately before any action was
taken pursuant hereto.


                                      -8-
<PAGE>   9




         IN WITNESS WHEREOF, the Corporation has executed this Certificate of
Designation as of the 14th day of December, 1998.


TOREADOR ROYALTY CORPORATION



By: /s/ G.T. GRAVES III
    ------------------------------------- 
    Name:  G. Thomas Graves III
    Title: President and Chief Executive Officer









                                      -9-
<PAGE>   10

                                                                       EXHIBIT A


                              NOTICE OF CONVERSION

The undersigned hereby elects to convert shares of Series A Convertible
Preferred Stock (the "Preferred Stock"), represented by stock certificate No(s).
(the "Preferred Stock Certificates"), into shares of common stock ("Common
Stock") of Toreador Royalty Corporation (the "Company") according to the terms
and conditions of the Certificate of Designation relating to the Preferred Stock
(the "Certificate of Designation"), as of the date written below. Capitalized
terms used herein and not otherwise defined shall have the respective meanings
set forth in the Certificate of Designation.

[ ] (check box if shares of Common Stock have been resold) The undersigned
represents that the shares of Common Stock to be issued by the Company hereby
have been resold or transferred by the undersigned in accordance with the
provisions of the prospectus included in the Registration Statement.

                         Date of Conversion:
                                                            ------------------
                         Number of Shares of
                         Preferred Stock to be Converted:
                                                            ------------------
                         Applicable Conversion Price:
                                                            ------------------

                         Number of Shares of
                         Common Stock to be Issued:
                                                            ------------------
                         Amount of Dividend
                         Accrued through the
                         Conversion Date:
                                                            ------------------

                         Name of Holder:
                                             ---------------------------------
                         Address:
                                             ---------------------------------

                                             ---------------------------------

                         Signature:
                                             ---------------------------------
                                             Name:
                                             Title:



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