The hypothesis that evolution of body size in birds was a random process coupled with an absolute lower boundary on body mass was tested using data on 6217 species of extant birds. The test was based on the fact that subclades within birds that have body masses much larger than this minimum should not have skewed log body mass distributions, while clades close to this boundary should. Bird species were classified into 23 orders suggested by Sibley and Monroe (1988). Thirteen orders that had average log body masses greater than the average for all birds had significantly skewed log body mass distributions. This is inconsistent with the hypothesis that evolution of body size in birds is random, but is constrained only at the smallest body masses. Most orders of birds cannot be considered random samples from the parental distribution of all birds. When the pattern of body mass evolution in birds is reconstructed using an estimate of the phylogenetic relationships among orders, there are many more instances where a large taxon putatively originated from a smaller one than vice versa. The non-random nature of body mass evolution in birds is consistent with models that postulate that evolution is constrained by the ability of individuals to turn resources into offspring.