Institutions shape social outcomes, yet institutions themselves are products of political choices. When institutional choices are determined by the same political and social processes that they shape, institutions are endogenously selected. Here I address the question of whether this endogenous institutional selection necessarily implies endogenous institutional effects. If it does, the use of institutional parameters as independent variables explaining policy outcomes and properties of the resulting political regimes, widespread in the literature on comparative political institutions, is hard to justify. I argue, however, that strategic choice of the rules of the game implies designers' ability to obtain their preferred institutional effects only under conditions of complete information. Under incomplete information, ex-post institutional effects do not need to be endogenous, since at the time of designing the rules the designers were not in position to control the selection of these effects. The reason why the choice of the rules does not imply the choice of their effects lies in the intervening and interactive (rather than additive) role played by the environmental parameters, including players' own characteristics, that are not revealed at the time of the institutional choice. Additionally to the model which illustrates the logic of the argument and the workings of intervening structural effects, I find supporting evidence in the processes of design of election laws in post-communist Europe, where stages of design and implementation followed each other in a very quick succession yet were characterized by substantial changes in manifested institutional preferences of the key political players.