Metabolic rates are correlated with many aspects of ecology, but how selection on different aspects of metabolic rates affects their mutual evolution is poorly understood. Using laboratory mice, we artificially selected for high maximal mass-independent metabolic rate (MMR) without direct selection on mass-independent basal metabolic rate (BMR). Then we tested for responses to selection in MMR and correlated responses to selection in BMR. In other lines, we antagonistically selected for mice with a combination of high mass-independent MMR and low mass-independent BMR. All selection protocols and data analyses included body mass as a covariate, so effects of selection on the metabolic rates are mass adjusted (that is, independent of effects of body mass). The selection lasted eight generations. Compared with controls, MMR was significantly higher (11.2%) in lines selected for increased MMR, and BMR was slightly, but not significantly, higher (2.5%). Compared with controls, MMR was significantly higher (5.3%) in antagonistically selected lines, and BMR was slightly, but not significantly, lower (4.2%). Analysis of breeding values revealed no positive genetic trend for elevated BMR in high-MMR lines. A weak positive genetic correlation was detected between MMR and BMR. That weak positive genetic correlation supports the aerobic capacity model for the evolution of endothermy in the sense that it fails to falsify a key model assumption. Overall, the results suggest that at least in these mice there is significant capacity for independent evolution of metabolic traits. Whether that is true in the ancestral animals that evolved endothermy remains an important but unanswered question.