Surfactants exhibit maxima in their critical micelle concentrations upon application of hydrostatic pressure, which is attributable to changes in their volumes of micellization from positive to negative values with increasing pressure. We present a direct molecular simulation analysis of the volumes of micellization of an anionic, cationic, and nonionic surfactant in aqueous solution at pressures up to 2500 bar. Excellent agreement with experiment is observed. A Kirkwood-Buff theory analysis based on proximal solvent distributions permits the breakdown of the volumes of micellization into constituent surfactant headgroup and tailgroup contributions. Although the micellization volume crossover is analogous to the transfer of an alkane from water to its pure liquid, significant differences are observed, including lower compressibilities of micelle volumes compared to that of the alkane liquid, negative partial compressibilites for anionic sulfated surfactant monomers, and large nonionic ethoxy headgroup contributions to the micellization volume.