National parks and other protected areas are at the forefront of global efforts to protect biodiversity and ecosystem services. However, not all protection is equal. Some areas are assigned strict legal protection that permits few extractive human uses. Other protected area designations permit a wider range of uses. Whether strictly protected areas are more effective in achieving environmental objectives is an empirical question: although strictly protected areas legally permit less anthropogenic disturbance, the social conflicts associated with assigning strict protection may lead politicians to assign strict protection to less-threatened areas and may lead citizens or enforcement agents to ignore the strict legal restrictions. We contrast the impacts of strictly and less strictly protected areas in four countries using IUCN designations to measure de jure strictness, data on deforestation to measure outcomes, and a quasi-experimental design to estimate impacts. On average, stricter protection reduced deforestation rates more than less strict protection, but the additional impact was not always large and sometimes arose because of where stricter protection was assigned rather than regulatory strictness per se. We also show that, in protected area studies contrasting y management regimes, there are y2policy-relevant impacts, rather than only y, as earlier studies have implied.