Rubin has offered multiple imputation as a general approach to inference from survey data sets with missing values filled in through imputation. In many situations the multiple imputation variance estimator is consistent. In turn, this observation has lent support to a number of complex applications. In fact, however, the multiple imputation variance estimator is inconsistent under some simple conditions. This article extends previous work of Rao and Shao and of Fay directed toward consistent variance estimation under wider conditions. Extensions of Rao and Shao's results tofractionally weighted imputationcombines the estimation efficiency of multiple imputation and the consistency of the Rao—Shao variance estimator.