This study uses simulation examples representing three types of treatment assignment mechanisms in data generation (the random intercept and slopes setting, the random intercept setting, and a third setting with a cluster-level treatment and an individual-level outcome) in order to determine optimal procedures for reducing bias and improving precision in each of these three settings. Evaluation criteria include bias, variance, MSE, confidence interval coverage rate, and remaining sample size. Specifically, the study evaluates the performance of (a) three variable selection procedures for propensity score models (confounder-covariate PS models [CF], outcome-covariate PS models [OC], and treatment-covariate PS models [TC]), (b) three methods of adjustment through outcome models (adjusting for propensity scores [PS], adjusting for propensity scores in combination with prognostic scores [PS+Prog], and adjusting for propensity scores in combination with strong outcome predictors [PS+Cov]), and (c) four model specifications for the propensity score models and the prognostic score models (the RIS models with cross-level interactions [RIS Interaction], the RIS models without cross-level interactions [RIS], the RI models without cross-level interactions [RI], and the single-level models [Single]). For the last three types of model specification, the effect of omitting the cluster-level covariates is also under investigation (RISC, RI-C, Single-C). The RIS model specification will not be considered in the RI setting; the RIS and RI model specifications will not be considered in the third setting with cluster-level treatment assignment. Propensity scores and prognostic scores are adjusted through either nonparametric stratification or parametric covariance adjustment. (Contains 5 tables and 3 figures.)