Although deletion of cases is still a common method of dealing with item nonresponse, imputation is a major alternative. With traditional methods of imputation, though, the usual variance formulas understate the variance of estimates. This paper proposes that items be imputed from distributions more diffuse than those of the real data, thereby compensating for the underestimation of variance by the usual formulas. The impact on covariances is considered in the design of the method. The method is intended for use by data analysts applying techniques based on functions of first and second moments of means only.