We discuss the properties of an incompatible Gibbs sampler widely used for multiple imputations. The iterative (or chained) imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling problem with relatively simple univariate regressions. The imputation distribution is then defined as the stationary (invariant) distribution of the corresponding Markov chain (an incompatible Gibbs sampler). We begin to characterize the convergence and stationary distributions of iterative imputations and their statistical properties.  The central analysis lies in creating a coupling of two Markov processes. The results and analysis techniques can be applicable to studies that involve modeling through conditional distributions in general.