The relations between rationality and optimizationhave been widely discussed in the wake of HerbertSimon's work, with the common conclusion that therationality concept does not imply the optimizationprinciple. The paper is partly concerned with addingevidence for this view, but its main, more challengingobjective is to question the converse implication fromoptimization to rationality, which is accepted even bybounded rationality theorists. We discuss three topicsin succession: (1) rationally defensible cyclicalchoices, (2) the revealed preference theory ofoptimization, and (3) the infinite regress ofoptimization. We conclude that (1) and (2) provideevidence only for the weak thesis that rationalitydoes not imply optimization. But (3) is seen todeliver a significant argument for the strong thesisthat optimization does not imply rationality.