We perform a block-averaging and extrapolation analysis of fast-switching free-energy difference (DeltaF) estimates for a computer-modeled, fully solvated ethane <----> methanol transformation. The results suggest that the analysis can greatly reduce the 'finite-sampling errors in DeltaF estimated from a small number of very fast switches. This error, which can be many times k(B)T, is the difference between an estimate based on a finite amount of data and that from an infinite data set; it is inherent in the DeltaF calculations. Our blocking/extrapolation procedure appears to be particularly useful for broad, non-Gaussian distributions of data which typically produce large finite-sampling errors. (C) 2002 Published by Elsevier Science B.V.