This paper introduces a general method to convert a model defined by moment conditions involving both observed and unobserved variables into equivalent moment conditions involving only observable variables. This task can be accomplished without introducing infinite-dimensional nuisance parameters using a least-favourable entropy-maximising distribution. We demonstrate, through examples and simulations, that this approach covers a wide class of latent variables models, including some game-theoretic models and models with limited dependent variables, interval-valued data, errors-in-variables, or combinations thereof. Both point- and set-identified models are transparently covered. In the latter case, the method also complements the recent literature on generic set-inference methods by providing the moment conditions needed to construct a GMM-type objective function for a wide class of models. Extensions of the method that cover conditional moments, independence restrictions and some state-space models are also given.