Research has demonstrated that possession exerts a potent influence on stimulus processing, such that objects are categorized more rapidly when owned-by-self than when they belong to other people. Outstanding theoretical questions remain, however, regarding the extent of this self-prioritization effect. In particular, does ownership enhance the processing of objects regardless of their valence or is self-prioritization restricted to only desirable items? To address this issue, here we explored the speed with which participants categorized objects (i.e., desirable and undesirable posters) that ostensibly belonged to the self and a best friend. In addition, to identify the cognitive processes supporting task performance, data were submitted to a hierarchical drift-diffusion model (HDDM) analysis. The results revealed a self-prioritization effect (i.e., RTself < RTfriend) for desirable posters that was underpinned by differences in the efficiency of stimulus processing. Specifically, decisional evidence was extracted more rapidly from self-owned posters when they were desirable than undesirable, an effect that was reversed for friend-owned posters. These findings advance understanding of when and how valence influences self-prioritization during decisional processing.