This study addressed the question of whether an overall preference for a suboptimal choice, previously found in pigeons (Stagner and Zentall, 2010), would be replicated with five brushtail possums. In Part One of this experiment possums responded on a concurrent-chain procedure where both alternatives had fixed-ratio 1 schedules in the initial link and a fixed-interval 10s in the terminal link. Two stimuli outcomes (four line orientations) are presented on the alternatives based on a probability of 0.20 or 0. 80. The left produced a discriminative stimulus with the right reinforcing on half of trials (20:50). Three of the five possums showed a consistent preference for the optimal alternative (50%), while the others showed a preference for the suboptimal (20%). When data was averaged possums showed a preference for the optimal alternative, which was not consistent with Stagner and Zentall’s (2010) earlier findings. Part Two of this investigation replicated Gipson, Alessandri, Miller and Zentall (2009), probabilities of stimuli appearing were changed to 50/50, with a discriminative stimulus on the left alternative and the probability of reinforcement on the optimal alternative increased to 75% (50:75). The discriminative stimuli were now more predictable than previously, when this was not present all possums showed a preference for the suboptimal alternative. When discriminative stimuli were associated with both alternatives (20:50), replicating Stagner, Laude and Zentall (2012), all possums showed all possums optimal preferences. An overall preference for the optimal alternative, seen during this study, is consistent with the findings reported in a more recent study by Trujano and Orduña’s (2015) with rats. This overall optimal preference is somewhat consistent with optimal foraging theory, however, this does not account for the suboptimal choices made by some possums. The suboptimal preferences seen by two possums in Part One and all in Part Two also loosely support previous findings that pigeons are under the control of discriminative stimuli.