Revealed preference theory is brought to bear on the problem of recovering approximate parametric preferences from consistent and inconsistent consumer choices. We propose measures of the incompatibility between the revealed preference ranking implied by choices and the ranking induced by the considered parametric preferences. These incompatibility measures are proven to characterize well-known inconsistency indices. We advocate a recovery approach that is based on such incompatibility measures and demonstrate its applicability for misspecification measurement and model selection. Using an innovative experimental design, we empirically substantiate that the proposed revealed-preference-based method predicts choices significantly better than a standard distance-based method.