It is argued that if we compute self-other agreement on some personality traits then we possess no or very little information about the individuals who are the targets of this judgment. This idea is largely based on two separate ways of computing self-other agreement: trait agreement (rT) and profile agreement (rP), which are typically associated with two different trait-centered and person-centered approaches in personality research. Personality traits of 4,115 targets from Czech, Belgian, Estonian, and German samples were rated by themselves and knowledgeable informants. We demonstrate that trait agreement can be partialled into individual contributions so that it is possible to show how much each individual pair of judges contributes to agreement on a particular trait. Similarly, it is possible to decompose agreement between two personality profiles into the individual contributions of traits from which these profiles are assembled. If normativeness is separated from distinctiveness of personality scores and individual profiles are ipsatized, then mean profile agreement r ̅_P becomes identical to mean trait agreement r ̅_T. The views that trait-by-trait analysis does not provide information regarding accuracy level of a particular pair of judges and profile analysis does not permit assessment of the relative contributions of traits to overall accuracy are not supported.