Accountability systems that measure student learning rather than student achievement have the potential to more accurately evaluate school quality. However, one methodological concern has remained surprisingly absent from discussions of value-added modeling. Standardized assessments that exhibit either positive or negative correlations between achievement and achievement gains will produce value-added estimates that contradict actual patterns of school effectiveness. This study uses student-level state assessment data to explore the ramifications of these relationships for value-added indicators. Within this state's assessment, the author finds strong negative relationships between achievement and subsequent achievement gains--initially low-scoring students appeared to gain more than their high-achieving peers. Because students are not randomly assigned to schools by achievement, these child-level correlations strongly influence school-level value-added estimates, in some cases quite dramatically. However, the manifestation of these relationships varies across four different analytic techniques, depending on how a particular approach modeled the associations between initial status and gain. (Contains 6 tables, 2 figures and 4 notes.)