Well-chosen covariates boost the design sensitivity of individually and cluster-randomized trials. We provide guidance on covariate selection generating an extensive compilation of single- and multilevel design parameters on student achievement. Embedded in psychometric heuristics, we analyzed (a) covariate "types" of varying bandwidth-fidelity, namely domain-identical (IP), cross-domain (CP), and fluid intelligence (Gf) pretests, as well as sociodemographic characteristics (SC); (b) covariate "combinations" quantifying incremental validities of CP, Gf, and/or SC beyond IP; and (c) covariate "time lags" of 1-7 years, testing validity degradation in IP, CP, and Gf. Estimates from six German samples (1868 [less than or equal to] N [less than or equal to] 10,543) covering various outcome domains across grades 1-12 were meta-analyzed and included in precision simulations. Results varied widely by grade level, domain, and hierarchical level. In general, IP outperformed CP, which slightly outperformed Gf and SC. Benefits from coupling IP with CP, Gf, and/or SC were small. IP appeared most affected by temporal validity decay. Findings are applied in illustrative scenarios of study planning and enriched by comprehensive Online Supplemental Material (OSM) accessible via the Open Science Framework (OSF; https://osf.io/nhx4w).