Purely statistical models have accounted for infants’ early ability to segment words out of fluent speech, with Bayesian models doing the best (Goldwater et al. 2009). Yet these models often incorporate unlikely assumptions, such as children having unlimited processing and memory resources and knowing the phonemes in their native language. Following Pearl, et al. (2011), we explore the impact of the former two assumptions on Bayesian learners, and additionally investigate the impact of the first assumption. We find a significant “Less is More” effect (Pearl et al 2011; Newport 1990) where memory and processing constraints appear to help, rather than hinder, performance. Further this effect is more robust than earlier results and we suggest this is due a relaxing of the assumption of phonemic knowledge, demonstrating the importance of modeling assumptions. Using more cognitively plausible assumptions can improve our understanding of language acquisition.