We know from the Head Start Impact Study (HSIS) that having access to Head Start improves children’s preschool experiences and school readiness, with some advantages persisting through first grade (Puma et al, 2010).  That said, scholars and practitioners alike have wondered whether impacts might be larger or more persistent for those who participate in high quality Head Start.  Despite the importance of this topic to policy and practice, to date the HSIS has not sought to answer the question primarily because of the analytic challenges involved in doing so.  A main challenge is that children who participate in high quality Head Start are likely to differ from those who participate in lower quality Head Start in important ways that relate to their outcomes, independently of the Head Start program.  In order to retain the strength of the experimental design in exploring the role of Head Start quality in influencing impacts, we use a creative approach to creating and analyzing subgroups.  Specifically, we use exogenous, baseline characteristics to identify subgroups of treatment group children who do not participate in Head Start (i.e., no-shows) and those in varying levels of Head Start quality and their counterparts in the control group (as first elaborated in Peck, 2003).  Doing so allows us to capitalize on the experimental design while analyzing the impacts of a characteristic (in this case Head Start quality) observed after the point of random assignment.  The presentation will focus on details of the analytic process and how it is applied to the Head Start data.