Objective: Conventional measures of self‐report bias implicitly assume consistent patterns of overclaiming across individuals. We contrast this with the effects of individual differences in views of trait desirability on overclaiming, which we label idiographically desirable responding (IDR). Method: We obtained self‐reports and peer reports of trait levels on mixed‐sex samples of undergraduates (N = 352) and middle‐aged community members (N = 541), with an additional performance‐based assessment in the latter sample. Results: Compared to conventional measures of bias, individual differences in trait desirability ratings identified an independent and comparatively large amount of the variance in overclaiming for personality and physical attractiveness. The importance of IDR was confirmed by the replication of these results for intelligence, for which both peer‐ratings and performance data were available. Individuals differed in the extent to which they rely on IDR, with these differences indexed by the correlation between views of the desirability of a given trait and the extent to which one overclaimed that trait. Individuals who were more prone to overclaim in this fashion exhibited higher self‐esteem as well as higher scores on questionnaire measures of socially desirable responding. Conclusion: Overclaiming of traits resulted both from the patterns of biases identified by conventional overclaiming measures and from individual differences in perceptions of what traits are most desirable. Copyright © 2013 John Wiley & Sons, Ltd.