The allometric relationship between brain and body size among vertebrates is often considered a manifestation of evolutionary constraints. However, birds and mammals have undergone remarkable encephalization, in which brain size has increased without corresponding changes in body size. Here, we explore the hypothesis that a reduction of phenotypic integration between brain and body size has facilitated encephalization in birds and mammals. Using a large dataset comprising 20,213 specimens across 4,587 species of jawed vertebrates, we show that the among-species (evolutionary) brain-body allometries are remarkably constant, both across vertebrate classes and across taxonomic levels. Birds and mammals, however, are exceptional in that their within-species (static) allometries are shallower and more variable than in other vertebrates. These patterns are consistent with the idea that birds and mammals have reduced allometric constraints that are otherwise ubiquitous across jawed vertebrates. Further exploration of ontogenetic allometries in selected taxa of birds, fishes and mammals reveals that birds and mammals have extended the period of fetal brain growth compared to fishes. Based on these findings, we propose that avian and mammalian encephalization has been contingent on increased variability in brain growth patterns.