In typical implementations of multiple imputation for missing data, analysts create m completed datasets based on approximately independent draws of imputation model parameters. We use theoretical arguments and simulations to show that, provided m is large, the use of independent draws is not necessary. In fact, appropriate use of dependent draws can improve precision relative to the use of independent draws. It also eliminates the sometimes difficult task of obtaining independent draws; for example, in fully Bayesian imputation models based on MCMC, analysts can avoid the search for a subsampling interval that ensures approximately independent draws for all parameters. We illustrate the use of dependent draws in multiple imputation with a study of the effect of breast feeding on children’s later cognitive abilities.