WARNING: THE EDGAR SYSTEM ENCOUNTERED ERROR(S) WHILE PROCESSING THIS SCHEDULE.
<TABLE> <S> <C>
<ARTICLE> 6
<RESTATED>
<CIK> 0001057943
<NAME> NUVEEN TAX-FREE UNIT TRUST
<SERIES> Series 1013
<NAME> CALIFORNIA INSURED TRUST
<NUMBER> 306
<MULTIPLIER> 1
<CURRENCY> U.S. DOLLARS
<FISCAL-YEAR-END> JUN-30-2000
<PERIOD-START> JUL-01-1999
<PERIOD-END> JUN-30-2000
<PERIOD-TYPE> YEAR
<EXCHANGE-RATE> 1
<INVESTMENTS-AT-COST> 2,037,058
<INVESTMENTS-AT-VALUE> 1,883,850
<RECEIVABLES> 28,799
<ASSETS-OTHER> 0
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 1,914,875
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 21,478
<TOTAL-LIABILITIES> 21,478
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 0
<SHARES-COMMON-STOCK> 21,445
<SHARES-COMMON-PRIOR> 24,850
<ACCUMULATED-NII-CURRENT> 9,779
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> -41,262
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> -153,208
<NET-ASSETS> 1,893,397
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 110,020
<OTHER-INCOME> 0
<EXPENSES-NET> 5,305
<NET-INVESTMENT-INCOME> 104,715
<REALIZED-GAINS-CURRENT> -41,262
<APPREC-INCREASE-CURRENT> -62,100
<NET-CHANGE-FROM-OPS> 1,353
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> 106,814
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 25,000
<NUMBER-OF-SHARES-REDEEMED> 3,555
<SHARES-REINVESTED> 0
<NET-CHANGE-IN-ASSETS> -392,264
<ACCUMULATED-NII-PRIOR> 11,878
<ACCUMULATED-GAINS-PRIOR> 0
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 0
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 0
<AVERAGE-NET-ASSETS> 0
<PER-SHARE-NAV-BEGIN> 0
<PER-SHARE-NII> 0
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> 0
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 0
<EXPENSE-RATIO> 0
[AVG-DEBT-OUTSTANDING] 0
[AVG-DEBT-PER-SHARE] 0
</TABLE>