Various neuroanatomical volume measures (NVMs) are frequently used as proxies for intelligence in comparative studies, such as the size of the brain, neocortex, and hippocampus, either absolute or controlled for other size measures (e.g., body size, or rest of the brain). Mean species NVMs are moderately correlated with aggregate general intelligence (G), however G and NVMs are yet to be compared in their evolutionary patterns (e.g., conservatism and evolutionary rates) and processes (i.e., their fit to diverse models of evolution reflecting selection regimes). Such evolutionary information is valuable for examining convergence in the evolutionary history among traits and is not available from simple correlation coefficients. Considering accumulating evidence that non-volumetric neurological measures may be as important as (or more so than) volumetric measures as substrates of intelligence, and that certain NVMs negatively predict neuronal density, we hypothesized that discrepancies would be found in evolutionary patterns and processes of G compared to NVMs. We collated data from the literature on primate species means for G, the volumes of the brain, neocortex, cerebellum, and hippocampus, and body mass, and employed phylogenetic comparative methods that examine phylogenetic signal (λ, K), evolutionary rates (σ2), and several parameters of evolutionary models (Brownian motion, Early-burst, acceleration, and Ornstein-Uhlenbeck). Evolutionary rates and acceleration trends were up to an order of magnitude higher for G than for most NVMs, and a strong selection optimum toward which clades evolved was found for G, whereas NVMs conformed mostly to Brownian motion. Brain size was the most contrasting NVM compared to intelligence across most phylogenetic indices examined, showing signs of deceleration and extreme conservativeness. Only certain operationalizations of neocortical and hippocampal volume showed convergence with G, albeit still notably weakly. The NVM with results that most strongly approached the patterns identified for G is residual cerebellar size (relative to body size). In comparison to the most commonly used volumetric measures (operationalization of brain and neocortex size), G must be seen as an evolutionarily labile trait under considerable selection pressure, necessitating that the role of the cerebellum be more aptly recognized and that other neurological factors be invoked as potential substrates for its evolutionary trajectory.