Human culture signifies the emergence of an entirely new domain of existence: an event in natural history that is paralleled only by the Cambrian Explosion in terms of creativity and scope. The question of how human culture—as opposed to its animal counterparts—came to become open-endedly creative and cumulative is therefore one of wide and general scientific importance. Several causal factors have been proposed to date to explain this unique quality, including population size, transmission fidelity, pedagogy, and creativity. Inquiries, however, tend to focus exclusively on one factor at a time, leaving us blind to important issues regarding their relative roles and combined action. We here combine two models, one focusing on population size and the other on imitation fidelity, as constraints and enablers of evolutionary cumulativity. We explore how these factors interact to promote and inhibit evolutionary cumulativity and how the synthetic model compares to the original models individually and to empirical and experimental data. We report several findings that do not emerge in the models that we combine individually. For example, group size is found to be important for small but not for larger groups, an observation that moreover substantially improves agreement with data.