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The present study evaluated the ability of item–level bifactor models (a) to provide an alternative explanation to current theories of higher order factors of personality and (b) to explain socially desirable responding in both job applicant and non–applicant contexts. Participants (46% male; mean age = 42 years, SD = 11) completed the 200–item HEXACO Personality Inventory–Revised either as part of a job application (n = 1613) or as part of low–stakes research (n = 1613). A comprehensive set of invariance tests were performed. Applicants scored higher than non–applicants on honesty–humility (d = 0.86), extraversion (d = 0.73), agreeableness (d = 1.06), and conscientiousness (d = 0.77). The bifactor model provided improved model fit relative to a standard correlated factor model, and loadings on the evaluative factor of the bifactor model were highly correlated with other indicators of item social desirability. The …