Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept in social choice theory. However, the concept of strategy-proofness has serious drawbacks. First, announcing one's true preference may not be a unique dominant strategy, and using the wrong dominant strategy may lead to the wrong outcome. Second, almost all strategy-proof mechanisms have a continuum of Nash equilibria, and most of which produce the wrong outcome. Third, experimental evidence shows that most of the strategy-proof mechanisms do not work well. We argue that a possible solution to this dilemma is to require double implementation in Nash equilibrium and in dominant strategies, which we call secure implementation. We characterize environments where secure implementation is possible, and compare it with dominant strategy implementation. An interesting example of secure implementation is a Groves mechanism when preferences are single-peaked.