In a set-target game, two players choose elements in some set X, and payoffs depend on whether the value of some function of these choices lies in a target set T. Typically, a set-target game has a continuum of Nash equilibria. Replacing the deterministic set T by a stochastic one and then shrinking the noise to zero may serve as a tool for equilibrium-selection. This smoothing procedure leads to a unique prediction if a certain (easy to verify) condition holds. In this case, smoothing leads to the outcome of the Nash bargaining solution. Otherwise, multiple points may be supported by perturbations