Abstract Multi-wave-cross-lagged-panel models (CLPMs) of directional ordering are a focus of much controversy in educational psychology and more generally. Extending traditional analyses, methodologists have recently argued for including random intercepts and lag2 effects between non-adjacent waves and giving more attention to controlling covariates. However, the related issues of appropriate time intervals between waves (lag1 intervals across waves) and the possibility of contemporaneous (lag0) effects within each wave are largely unresolved. Although philosophers, theologians, and scientists widely debate sequential (lagged) and simultaneous (lag0) theories of causality, CLPM researchers have mostly ignored contemporaneous effects, arguing causes must precede effects. In a substantive-methodological synergy, we integrated these issues and designed new structural equation models to reanalyze one of the strongest CLPM studies of academic self-concept (ASC) and achievement (five annuals of mathematics data; 3527 secondary school students). A taxonomy of models incorporating various combinations of lag0, lag1, and lag2 effects, random intercepts, and covariates consistently supported a priori reciprocal effect model (REM) predictions—medium or large reciprocal effects of ASC and achievement on each other. Consistent with self-concept theory, effects of ASC on achievement evolved over time (lag1, not lag0 effects), whereas effects of achievement on ASC effects were more contemporaneous (lag0, not lag1 effects). We argue that lag0 effects reflect proximal events occurring subsequent to the previous data wave, suggesting the need for shorter intervals but also leaving open the possibility of contemporaneous effects that are truly instantaneous. We discuss limitations and future directions but also note the broad applicability of our statistical models.