There may be many game forms that implement a particular social choice correspondence under Nash equilibrium; some of these game forms may produce undesirable outcomes when viewed against other criteria. The authors introduce a concept of constitutional implementation to capture these ideas of socially desirable outcomes. They view a constitution as a pre-existing collection of rules that specify power (that is, range of outcomes) for subsets of the set of players. Hence, they can model a constitution as an effectivity function. The main results of the paper are determining necessary and sufficient conditions for social choice correspondences to admit a game form that satisfies the constitutional effectivity function. More precisely, the authors introduce three levels of constitutional implementation: weak, if the effectivity function of the game form is a sub-correspondence of the effectivity function of the social choice correspondence; plain, if the two effectivity functions are equal, and almost, which is the weakly constitutional condition plus the requirement that the sets of winning coalitions of the game form and the social choice correspondence are equal. The authors then determine necessary and sufficient conditions for almost constitutional implementation and elaborate some consequences of their result.