Developmental stability and canalization describe the ability of developmental systems to minimize phenotypic variation in the face of stochastic micro-environmental effects, genetic variation and environmental influences. Canalization is the ability to minimize the effects of genetic or environmental effects, while developmental stability is the ability to minimize the effects of micro-environmental effects within individuals. Despite much attention, the mechanisms that underlie these two components of phenotypic robustness remain unknown. We investigated the genetic structure of phenotypic robustness in the Collaborative Cross (CC) mouse reference population. We analyzed the magnitude of fluctuating asymmetry (FA) and among-individual variation of cranial shape in reciprocal crosses among the eight parental strains, by using geometric morphometrics and a diallel analysis based on a Bayesian approach. Significant differences among genotypes were found for both measures, though they were poorly correlated at the level of individuals. An overall positive effect of inbreeding was found for both components of variation. The strain CAST/EiJ exerted a positive additive effect on FA and, to a lesser extent, among-individual variance. Sex and other strain specific effects were not significant. Neither FA nor among-individual variation was associated with phenotypic extremeness. Our results support the existence of genetic variation for both developmental stability and canalization. This finding is important because robustness is a key feature of developmental systems. Our finding that robustness is not related to phenotypic extremeness is consistent with theoretical work that suggests that its relationship to stabilizing selection is not straightforward.