Since creative individuals invest in unproven ideas at the expense of propagating proven ones, excess creativity can be detrimental to society; moreover, some individuals benefit from creativity without being creative themselves by copying creators. This paper builds on previous studies of how societies evolve faster by tempering the novelty-generating effects of creativity with the novelty-preserving effects of imitation. It was hypothesized that (1) this balance can be achieved through self-regulation (SR) of creativity, by varying how creative one is according to the value of one’s creative outputs, and (2) that the social benefit of SR is affected by the openness of the space of possible ideas. These hypotheses were tested using EVOC, an agent-based model of cultural evolution in which each agent self-regulated its invention-to-imitation ratio as a function of the fitness of its inventions. We compared SR to non-SR societies, and compared societies in which the space of possible ideas was open-ended because agents could chain simple ideas into complex ones, to societies without chaining, for which the space of possible ideas was fixed. Agents in SR societies gradually segregated into creators and imitators, and changes in diversity were rapider and more pronounced than non-SR. The mean fitness of ideas was higher in SR than non-SR societies, but this difference was temporary without chaining whereas it was permanent with chaining. We discuss limitations of the model and possible social implications of the results.