Prior work has shown that the degree of basicranial flexion among primates is determined by relative brain size, with anatomically modern humans possibly having a less flexed basicranium than expected for their relative brain size. Basicranial flexion has also been suggested to be adaptive in that it maintains a spheroid brain shape, thereby minimizing connections between different parts of the brain. In addition, it has been argued that the degree of flexion might be constrained such that increases in relative brain size beyond that seen in Australopithecus africanus were accommodated by mechanisms other than basicranial flexion. These hypotheses were evaluated by collating an extensive data set on basicranial flexion and relative brain size in primates and other mammals. The data were analyzed using standard least squares regression, geometric and curvilinear modeling, and phylogenetically independent contrasts (PICs). Geometric modeling does not support the hypothesis that flexion is an adaptation that facilitates enlargement of a spheroid brain. Whether humans have a less flexed basicranium than expected for their relative brain size depends on the phylogenetic vantage point from which it is evaluated. They are as flexed as expected for a descendant of the last common ancestor of the Paranthropus-Homo clade, but their degree of flexion cannot be predicted from the basal hominoid node, even if their relative brain size is specified. Humans undoubtedly occupy an unusual part of morphospace in terms of basicranial flexion and relative brain size, but this does not mean that their degree of flexion is or is not constrained. Curvilinear regression models and standard linear regression models describe the relationship between flexion and relative brain size equally well. Hypotheses that the degree of flexion is or is not constrained cannot be discriminated at present. Consideration of recently published ontogenetic data in the context of the interspecific data for adults suggests that much of the variance in basicranial flexion can still be explained as a mechanical consequence of brain enlargement relative to basicranial length.