We show that a solution to the problem of mechanism selection by an informed principal exists in a large class of environments with generalized private values: the agents' payoff functions are independent of the principal's type. The solution is an extension of Maskin and Tirole's (1990) strong unconstrained Pareto optimum. Our main condition for existence is that given any type profile the best possible outcome for the principal is the worst possible outcome for all agents. This condition is satisfied in most market environments. We also compute some examples of strong unconstrained Pareto optima.