Attending preschool improves children's kindergarten readiness, but the cognitive outcomes of preschool attenders and non-attenders tend to converge partially or fully in elementary school. In older programs, most of the non-attender "catch up" occurs in kindergarten (Li et al., 2016), but evidence from today's programs is relatively sparse. Using data on approximately 5,000 Boston Public School prekindergarten appliers and a quasi-experimental approach, we examine convergence patterns in the K-3 literacy outcomes of prekindergarten attenders and non-attenders. Consistent with the previous literature, we find that most of the convergence in K-3 literacy outcomes occurs in kindergarten. Our findings suggest that detailed investigations into the kindergarten teaching and learning context may be particularly important for solving the widely noted preschool convergence pattern. (author abstract)