WARNING: THE EDGAR SYSTEM ENCOUNTERED ERROR(S) WHILE PROCESSING THIS SCHEDULE.
<TABLE> <S> <C>
<ARTICLE> 6
<RESTATED>
<CIK> 0000941226
<NAME> NUVEEN TAX-FREE UNIT TRUST
<SERIES> Series 801
<NAME> CONNECTICUT TRADITIONAL TRUST
<NUMBER> 273
<MULTIPLIER> 1
<CURRENCY> U.S. DOLLARS
<FISCAL-YEAR-END> APR-30-2000
<PERIOD-START> MAY-01-1999
<PERIOD-END> APR-30-2000
<PERIOD-TYPE> YEAR
<EXCHANGE-RATE> 1
<INVESTMENTS-AT-COST> 2,902,725
<INVESTMENTS-AT-VALUE> 2,964,354
<RECEIVABLES> 43,268
<ASSETS-OTHER> 0
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 3,007,622
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 15,967
<TOTAL-LIABILITIES> 15,967
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 0
<SHARES-COMMON-STOCK> 29,843
<SHARES-COMMON-PRIOR> 30,290
<ACCUMULATED-NII-CURRENT> 34,125
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> 40,414
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 61,629
<NET-ASSETS> 2,991,655
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 170,132
<OTHER-INCOME> 0
<EXPENSES-NET> 5,370
<NET-INVESTMENT-INCOME> 164,762
<REALIZED-GAINS-CURRENT> 1,708
<APPREC-INCREASE-CURRENT> -193,176
<NET-CHANGE-FROM-OPS> -26,706
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> 165,809
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 35,000
<NUMBER-OF-SHARES-REDEEMED> 5,157
<SHARES-REINVESTED> 0
<NET-CHANGE-IN-ASSETS> -237,555
<ACCUMULATED-NII-PRIOR> 35,172
<ACCUMULATED-GAINS-PRIOR> 38,706
<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>
