Insular gigantism—evolutionary increases in body size from small-bodied mainland ancestors—is a conceptually significant, but poorly studied, evolutionary phenomenon. Gigantism is widespread on Mediterranean islands, particularly among fossil and extant dormice. These include an extant giant population of Eliomys quercinus on Formentera, the giant Balearic genus † Hypnomys and the exceptionally large † Leithia melitensis of Pleistocene Sicily. We quantified patterns of cranial and mandibular shape and their relationships to head size (allometry) among mainland and insular dormouse populations, asking to what extent the morphology of island giants is explained by allometry. We find that gigantism in dormice is not simply an extrapolation of the allometric trajectory of their mainland relatives. Instead, a large portion of their distinctive cranial and mandibular morphology resulted from the population- or species-specific evolutionary shape changes. Our findings suggest that body size increases in insular giant dormice were accompanied by the evolutionary divergence of feeding adaptations. This complements other evidence of ecological divergence in these taxa, which span predominantly faunivorous to herbivorous diets. Our findings suggest that insular gigantism involves context-dependent phenotypic modifications, underscoring the highly distinctive nature of island faunas.