Sperm size is one of the most diverse traits across the animal tree of life, but even more variable perhaps is the shape of the cell. In many lineages, the cell is composed of a head (which contains the nuclear material), a midpiece (which contains the mitochondria), and a flagellum (which propels the cell). As each part of the sperm has a unique function, it seems likely that each component may follow a different evolutionary trajectory. However, genetic correlations between these cellular components could result in correlated shifts in size of multiple parts of the cell. I tested these hypotheses by collecting sperm morphological data for 1194 vertebrate species. For each vertebrate class I measured the rate of evolution of the sperm head, midpiece, and flagellum and located evolutionary shifts in size for each of these components on the tree. I found that across animals the sperm midpiece evolves faster than both the head and flagellum, indicating strong selection for sperm energetics. Additionally, head length evolves slowly in almost all lineages, suggesting that its diversification may constrained by functional limitations. I found that branches which contained an evolutionary shift in the size of one sperm component often contained shifts in the size of other parts of the cell. This suggests that genetic correlations between the sperm components cause parts of the cell to have a concerted response to selection. These results suggest that while postcopulatory selection on specific components of sperm may result in faster rates of evolution, genetic correlations within the cell can either constrain or promote faster evolution of the other components of the sperm cell.