We have determined the variations in volume that occur during evolution in the buried core of three different families of proteins. The variation of the whole core is very small (approximately 2.5%) compared to the variation at individual sites (approximately 13%). However, by comparing our results to those expected from random sequences with no correlations between sites, we show that the small variation observed may simply be a manifestation of the statistical "law of large numbers" and not reflect any compensating changes in, or global constraints upon, protein sequences. We have also analysed in detail the volume variations at individual sites, both in the core and on the surface, and compared these variations with those expected from random sequences. Individual sites on the surface have nearly the same variation as random sequences (24% versus 28% variation). However, individual sites in the core have about half the variation of random sequences (13% versus 30%). Roughly, half of these core sites strongly conserve their volume (0 to 10% variation); one quarter have moderate variation (10 to 20%); and the remaining quarter vary randomly (20 to 40%). Our results have clear implications for the relationship between protein sequence and structure. For our analysis, we have developed a new and simple method for weighting protein sequences to correct for unequal representation, which we describe in an Appendix.