Afriat’s (Int Econ Rev 14(2): 460–472, 1973) critical cost efficiency index is often used to measure the extent to which experimental choice data violate the axioms of revealed preference. Under certain conditions, the index yields a value of one—which typically signifies rational choice—when, in fact, the choice violates the axioms. We term this a cost efficient violation (CEV) of the axioms, clarify the conditions under which it arises, and find that CEVs comprise the majority of violations in three of four studies reviewed. We suggest changes in experiment design to eliminate or reduce the likelihood of CEVs.