We investigate the causes of site-specific evolutionary-rate variation in influenza haemagglutinin (HA) between human and avian influenza, for subtypes H1, H3, and H5. By calculating the evolutionary-rate ratio, ω = dN/dS as a function of a residue's solvent accessibility in the three-dimensional protein structure, we show that solvent accessibility has a significant but relatively modest effect on site-specific rate variation. By comparing rates within HA subtypes among host species, we derive an upper limit to the amount of variation that can be explained by structural constraints of any kind. Protein structure explains only 20-40% of the variation in ω. Finally, by comparing ω at sites near the sialic-acid-binding region to ω at other sites, we show that ω near the sialic-acid-binding region is significantly elevated in both human and avian influenza, with the exception of avian H5. We conclude that protein structure, HA subtype, and host biology all impose distinct selection pressures on sites in influenza HA.