The concept of a dominance solvable voting scheme is presented as a weakening of the strategy-proofness requirement: it relies on successive elimination of dominated strategies and generalizes the well known concept of "sophisticated voting." Dominance solvable decision schemes turn out to contain many usual voting procedures such as voting by veto, kingmaker, and voting by binary choices. The procedure of voting by elimination is proved to be an anonymous dominance solvable voting scheme which always selects an efficient alternative.