Abstract Paunonen (2002) recently developed the Supernumerary Personality Inventory (SPI), a measure of 10 traits that have low loadings within the space of the Big Five personality factors. If the SPI personality traits are representative of the domain of non-Big Five personality traits, then the major source of the variance in the SPI traits would be expected to correlate strongly with the sixth factor of personality, Honesty-Humility. We tested this hypothesis using self-report measures (N=200) of the SPI traits, of the Big Five, and of the new six-dimensional (“HEXACO”) structure. Results indicated that the first unrotated factor underlying the 10 SPI traits was heavily saturated with variance from Honesty-Humility (r=.65). Nevertheless, the 10 SPI traits contained substantial amounts of unique variance not accounted for by the HEXACO or the Big Five variables, highlighting the importance of the facet-level assessment of personality traits.