The U.S. Bureau of Labor Statistics (BLS) faces sample size constraints when computing its Consumer Price Index (CPI-U). Price indices are a nonlinear function of prices, and while they are consistent, samples are not adequately large for them to be "close" to their asymptotic values. This study adjusts for finite sample bias by estimating the second order of a stochastic expansion of the index. From the beginning of 2000 to the end of 2003, we find approximately 62% of the difference between the BLS superlative index (CPI-C) and the CPI-U is the result of finite sample bias. The other 38% is commodity substitution bias.