The two-step hypothesis of Müllerian mimicry evolution states that mimicry starts with a major mutational leap between adaptive peaks, followed by gradual fine-tuning. The hypothesis was suggested to solve the problem of apostatic selection producing a valley between adaptive peaks, and appears reasonable for a one-dimensional phenotype. Extending the hypothesis to the realistic scenario of multidimensional phenotypes controlled by multiple genetic loci can be problematic, because it is unlikely that major mutational leaps occur simultaneously in several traits. Here we consider the implications of predator psychology on the evolutionary process. According to feature theory, single prey traits may be used by predators as features to classify prey into discrete categories. A mutational leap in such a trait could initiate mimicry evolution. We conducted individual-based evolutionary simulations in which virtual predators both categorize prey according to features and generalize over total appearances. We found that an initial mutational leap toward feature similarity in one dimension facilitates mimicry evolution of multidimensional traits. We suggest that feature-based predator categorization together with predator generalization over total appearances solves the problem of applying the two-step hypothesis to complex phenotypes, and provides a basis for a theory of the evolution of mimicry rings.