In general, the result of the elimination of weakly dominated strategies depends on order. We define nice weak dominance. Under nice weak dominance, order does not matter. We identify an important class of games under which nice weak dominance and weak dominance are equivalent, and so the order under weak dominance does not matter. For all games, the result of iterative nice weak dominance is an upper bound on the result from any order of weak dominance. The results strengthen the intuitive relationship between backward induction and weak dominance and shed light on some computational problems relating to weak dominance. Journal of Economic Literature Classification Number: C72. © 1997 Academic Press.