When divergent populations interbreed, their alleles are brought together in hybrids. In the initial F1 cross, most divergent loci are heterozygous. Therefore, F1 fitness can be influenced by dominance effects that could not have been selected to function well together. We present a systematic study of these F1 dominance effects by introducing variable phenotypic dominance into Fisher's geometric model. We show that dominance often reduces hybrid fitness, which can generate optimal outbreeding followed by a steady decline in F1 fitness, as is often observed. We also show that "lucky" beneficial effects sometimes arise by chance, which might be important when hybrids can access novel environments. We then show that dominance can lead to violations of Haldane's Rule (reduced fitness of the heterogametic F1) but strengthens Darwin's Corollary (F1 fitness differences between cross directions).Taken together, results show that the effects of dominance on hybrid fitness can be surprisingly difficult to isolate, because they often resemble the effects of uniparental inheritance or expression. Nevertheless, we identify a pattern of environment-dependent heterosis that only dominance can explain, and for which there is some suggestive evidence. Our results also show how existing data set upper bounds on the size of dominance effects. These bounds could explain why additive models often provide good predictions for later-generation recombinant hybrids, even when dominance qualitatively changes outcomes for the F1.