Five issues relative to the use of different Ordinary Least Squares (OLS) and Hierarchical Linear Modeling (HLM) models to identify effective schools and teachers were examined using data from all students in the Dallas (Texas) public schools in grade 3 in 1994 and grade 4 in 1995. OLS models using first- and second-order interactions produced results that were very close to those produced by two-level HLM models at the school level and two- and three-level HLM models at the teacher level. Most OLS regression and HLM models used in this study accounted for more than 70% of the variance in student achievement in reading and mathematics. Results produced by all the models were extremely consistent, and correlations produced by the various models were all generally above 0.90. Correlations of results with important school, teacher, and student-level contextual variables were negligible for all models, meaning that the various models produced results that were free from bias relative to important contextual variables. Correlations of results with prescore characteristics were negligible for all models, meaning that the various models produced results that were free from bias relative to the level of pretest scores. Taking all results into consideration, it is recommended that a two-level HLM model (student-school) be implemented to determine school effect, and that the empirical Bayes residuals from the model be adjusted with an adjustment for shrinkage to form the basis for estimates of teacher effect. Appropriate formulas for this task are included. (Contains 34 references.) (SLD)