The oxygen store/usage hypothesis suggests that larger animals are able to dive for longer and hence deeper because oxygen storage scales isometrically with body mass, whereas oxygen usage scales allometrically with an exponent <1 (typically 0.67-0.75). Previous tests of the allometry of diving tend to reject this hypothesis, but they are based on restricted data sets or invalid statistical analyses (which assume that every species provides independent information). Here we apply information-theoretic statistical methods that are phylogenetically informed to a large data set on diving variables for birds and mammals to describe the allometry of diving. Body mass is strongly related to all dive variables except dive:pause ratio. We demonstrate that many diving variables covary strongly with body mass and that they have allometric exponents close to 0.33. Thus, our results fail to falsify the oxygen store/usage hypothesis. The allometric relationships for most diving variables are statistically indistinguishable for birds and mammals, but birds tend to dive deeper than mammals of equivalent mass. The allometric relationships for all diving variables except mean dive duration are also statistically indistinguishable for all major taxonomic groups of divers within birds and mammals, with the exception of the procellariiforms, which, strictly speaking, are not true divers.