The HEXACO personality factors of Agreeableness‐versus‐Anger (A) and Honesty‐Humility (H) are interpreted as two complementary aspects of reciprocal altruistic tendency. Here we consider several ways of representing the positive associations between the defining traits of A and of H, through common factor analysis of self‐report HEXACO Personality Inventory—Revised (HEXACO‐PI‐R) facet scale scores (N≈ 111,000). We describe orthogonal solutions that differ in the extent to which H facets show secondary loadings on A (and vice versa), as well as an oblique solution compatible with a higher‐order “cooperativeness” factor. We discuss the psychological plausibility of these solutions, and we review research showing differential associations of several phenomena or outcomes with A and H. We conclude that the optimal representation of A/H trait associations is not yet known but that the value of separate A and H factor scales is well established.