In a broad class of situations not covered by the Gibbard-Satterthwaite Theorem it is shown that one cannot design a strategy-proof choice mechanism which attains Pareto optimal outcomes. The results are shown to be genetic in character--i.e., any nonmanipulable mechanism will attain nonoptimal outcomes virtually everywhere--and they cover, in particular, certain problems of allocating public and private goods. The analysis is carried out in transferable utility environments, and makes extensive use of the mechanisms recently introduced by Groves.