At the macroevolutionary level, one of the first and most important hypotheses that proposes an evolutionary tendency in the evolution of body sizes is "Cope's rule". This rule has considerable empirical support in the fossil record and predicts that the size of species within a lineage increases over evolutionary time. Nevertheless, there is also a large amount of evidence indicating the opposite pattern of miniaturization over evolutionary time. A recent analysis using a single phylogenetic tree approach and a Bayesian based model of evolution found no evidence for Cope's rule in extant mammal species. Here we utilize a likelihood-based phylogenetic method, to test the evolutionary trend in body size, which considers phylogenetic uncertainty, to discern between Cope's rule and miniaturization, using extant Oryzomyini rodents as a study model. We evaluated body size trends using two principal predictions: (a) phylogenetically related species are more similar in their body size, than expected by chance; (b) body size increased (Cope's rule)/decreased (miniaturization) over time. Consequently the distribution of forces and/or constraints that affect the tendency are homogenous and generate this directional process from a small/large sized ancestor. Results showed that body size in the Oryzomyini tribe evolved according to phylogenetic relationships, with a positive trend, from a small sized ancestor. Our results support that the high diversity and specialization currently observed in the Oryzomyini tribe is a consequence of the evolutionary trend of increased body size, following and supporting Cope's rule.