1. Trade-offs in resource allocation underline the evolution of life-history traits but their expression is frequently challenged by empirical findings. In large herbivores, males with large antlers or horns typically have high mating success. The fitness costs of large horns or antlers have rarely been quantified although they are controversial. 2. Here, using detailed longitudinal data on n = 172 bighorn (Ovis canadensis, Shaw) and the capture-mark-recapture methodology, we tested whether early horn growth leads to a survival cost in rams ('trade-off' hypothesis) or if males that can afford rapid horn growth survive better than males of lower phenotypic quality ('phenotypic quality' hypothesis). We also quantified how hunting increased survival costs of bearing large horns. 3. We found an age-specific relationship between horn growth and survival. In all age classes, natural survival was either weakly related to (lambs, adult rams) or positively associated (yearling rams) with early horn growth. Hunting mortality was markedly different from natural mortality of bighorn rams, leading to an artificial negative association between early horn growth and survival. Beginning at age 4, the yearly harvest rate ranged from 12% for males with the smallest horns up to more than 40% for males with the largest horns. 4. Growing large horns early in life is not related to any consistent survival costs, hence supporting the phenotypic quality hypothesis in males of a dimorphic and polygynous large herbivores. Rapid horn growth early in life is, however, strongly counter selected by trophy hunting. We suggest that horn size is a very poor index of reproductive effort and that males modulate their mating activities and energy allocation to horn growth to limit its impact on survival.