We test for the existence of a general factor of personality self-reports in HEXACO Personality Inventory—Revised (HEXACO-PI-R) facet scales, using two samples of persons who responded under normal conditions and two samples of persons who responded under conditions in which at least some participants would perceive some incentive to describe themselves favorably. Using bi-factor (or nested factor) modeling, we found that a truly general factor was not obtained in the “normal conditions” samples; instead, the putative general factor was a broad variant of Extraversion, leaving a smaller residual Extraversion factor. Moreover, the fit of the general factor model in these samples was poorer than that of a more parsimonious “blended variable” model that incorporated secondary loadings instead of a general factor. In the samples whose participants had some incentive to “fake good”, a truly general factor was obtained, and the fit of the general factor model was at least as good as that of the blended factor model. These results suggest that a general factor of personality self-reports does not typically emerge from HEXACO-PI-R facet scores obtained under normal conditions of responding and therefore that such a factor obtained under other conditions is not a general factor of personality.