The idea that demographic change may spur or slow down technological change has become widely accepted among evolutionary archaeologists and anthropologists. Two models have been particularly influential in promoting this idea: a mathematical model by Joseph Henrich, developed to explain the Tasmanian loss of culture during the Holocene; and an agent-based adaptation thereof, devised by Powell et al. to explain the emergence of modern behaviour in the Late Pleistocene. However, the models in question make rather strong assumptions about the distribution of skills among social learners and about the selectivity of social learning strategies. Here I examine the behaviour of these models under more conservative and, on empirical and theoretical grounds, equally reasonable assumptions. I show that, some qualifications notwithstanding, Henrich’s model largely withstands my robustness tests. The model of Powell et al., in contrast, does not–a finding that warrants a fair amount of skepticism towards Powell et al.’s explanation of the Upper Paleolithic transition. More generally, my evaluation of the accounts of Henrich and of Powell et al. helpfully clarify which inferences their popular models do and not support.