The consequences for organism fitness of mutations in a given protein are often thought to be determined to a significant extent by epistasis, that is, by the fact that the effect of a mutation may be strongly dependent on the previous mutational background. Actually, a given mutation could be deleterious or beneficial depending on the background, a situation known as 'sign epistasis'. Under pervasive sign epistasis, many mutational trajectories towards a 'fitter protein' will show a 'dip' in fitness and, it has been previously suggested, only a few trajectories will be available to Darwinian selection. In this issue of the Biochemical Journal, Zhang et al. explore how this simple picture needs to be modified when two rather general and important features are taken into account, namely that many proteins are promiscuous and that living organisms must survive and thrive in environments that change continuously. The multidimensional nature of epistasis for a protein involved in several tasks, together with the fact that different tasks may become critical for organism survival as environmental conditions change, is shown by Zhang et al. to contribute to eliminating fitness dead-ends in protein sequence space. Consequently, many alternative mutational trajectories should allow protein optimization for enhanced organism fitness under changing environmental conditions.