When is it beneficial to constrain creativity? Creativity thrives with freedom, but when people collaborate to create artifacts, there is tension between giving individuals freedom to revise, and protecting prior achievements. To test how imposing constraints may affect collective creativity, we performed cultural evolution experiments where participants collaborated to create melodies and images in chains. With melodies, we found that limiting step size (number of musical notes that can be changed) improved pleasantness ratings. Similar results were observed in cohorts of musicians, and with different selection regimes. This outcome was due to the tendency to overcrowd melodies. Interestingly, limiting step size in creating images consistently reduced pleasantness. These conflicting findings suggest that in domains such as music, where artifacts can be easily damaged, collective creativity may benefit from imposing small step sizes or limiting overcrowding. We discuss parallels with search algorithms and the evolution of conservative birdsong cultures.