A great deal o£ effort has gone into alleviating the regrettable consequences of the Gibbard-Satterthwaite Theorem: that every stable decisive social choice function is dictatorial. Thus, Kelly [12] explores the conse quences of relaxing decisiveness, while Peleg [14] and Dutta and Pattanaik [3] introduce various notions of strategic consistency, in which the sincere outcome stands in some determinate relation to the game outcome. This paper, draws upon both these lines of research.