A positive genetic correlation between basal metabolic rate (BMR) and maximal ([VO.sub.2]max) rate of oxygen consumption is a key assumption of the aerobic capacity model for the evolution of endothermy. We estimated the genetic ([V.sub.A], additive, and [V.sub.D], dominance), prenatal ([V.sub.N]), and postnatal common environmental ([V.sub.C]) contributions to individual differences in metabolic rates and body mass for a genetically heterogeneous laboratory strain of house mice (Mus domesticus). Our breeding design did not allow the simultaneous estimation of [V.sub.D] and [V.sub.N]. Regardless of whether [V.sub.D] or [V.sub.N] was assumed, estimates of [V.sub.A] were negative under the full models. Hence, we fitted reduced models (e.g., [V.sub.A] + [V.sub.N] + [V.sub.E] or [V.sub.A] + [V.sub.E]) and obtained new variance estimates. For reduced models, narrow-sense heritability ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) for BMR was [is less than] 0.1, but estimates of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for [VO.sub.2]max were higher. When estimated with the [V.sub.A] + [V.sub.E] model, the additive genetic covariance between [VO.sub.2]max and BMR was positive and statistically different from zero. This result offers tentative support for the aerobic capacity model for the evolution of vertebrate energetics. However, constraints imposed on the genetic model may cause our estimates of additive variance and covariance to be biased, so our results should be interpreted with caution and tested via selection experiments.