In this article we address a number of important issues that arise in the analysis of nonindependent data. Such data are common in studies in which predictors vary within “units” (e.g., within-subjects, within-classrooms). Most researchers analyze categorical within-unit predictors with repeated-measures ANOVAs, but continuous within-unit predictors with linear mixed-effects models (LMEMs). We show that both types of predictor variables can be analyzed within the LMEM framework. We discuss designs with multiple sources of nonindependence, for example, studies in which the same subjects rate the same set of items or in which students nested in classrooms provide multiple answers. We provide clear guidelines about the types of random effects that should be included in the analysis of such designs. We also present a number of corrective steps that researchers can take when convergence fails in LMEM models with too many parameters. We end with a brief discussion on the trade-off between power and generalizability in designs with “within-unit” predictors.