We propose strike mechanisms as a solution to the classical problem of Hurwicz and Schmeidler (1978) and Maskin (1999) according to which, in two-person societies, no Pareto efficient rule is Nash-implementable. A strike mechanism specifies the number of alternatives that each player vetoes. Each player simultaneously casts these vetoes and the mechanism selects randomly one alternative among the non-vetoed ones. For strict preferences over alternatives and under a very weak condition for extending preferences over lotteries, these mechanisms are deterministic-in-equilibrium. They Nash implement a class of Pareto efficient social choice rules called Pareto-and-veto rules. Moreover, under mild richness conditions on the domain of preferences over lotteries, any Pareto efficient Nash-implementable rule is a Pareto-and-veto rule and hence is implementable through a strike mechanism.