The Consumer Price Index estimation system currently uses a hybrid linearization random groups method to compute variances. This method was compared to a hybrid linearization method implemented using SUDAAN, a stratified random group method implemented using VPLX, and balanced repeated replication and unstratified jackknife methods implemented using WesVarPC. In this analysis, variances were computed for several index series using each candidate method. The methods were evaluated on the basis of their stability, which was used as a proxy for the variance of the variance estimates. The authors found that the stratified random group method implemented using VPLX was superior to the other candidates. This paper describes the candidate variance calculation methods. Results are given for each combination of studied index series and variance calculation method. The authors found several instances in which there was a breakdown in the assumptions that underlie linearization. One instance is described in detail. In addition, several non-numeric issues, such as computation time and variance computation cost are discussed.