The expectation maximization (EM) algorithm is a widely used maximum likelihood estimation procedure for statistical models when the values of some of the variables in the model are hidden. Very often, however, our aim is primarily to find a model that assigns values to the latent variables that have intended meaning for our data and maximizing expected likelihood only sometimes accomplishes this. Unfortunately, it is often very indirect or difficult to add even simple a priori information about latent variables without making models overly complex or intractable. In this paper, we present an efficient, principled way to inject constraints on the posteriors of latent variables into the EM algorithm. Our method can be viewed as a regularization of the posteriors of hidden variables, or alternatively as a restriction on the types of lower bounds used for maximizing data likelihood. Focusing on the alignment problem for statistical machine translation, we show that simple, intuitive posterior constraints can greatly improve the performance over standard baselines and be competitive with more complex, intractable models.