This study addressed statistical techniques that might ameliorate some of the sampling problems currently facing states with small populations participating in State National Assessment of Educational Progress (NAEP) assessments. The study explored how the application of finite population correction factors to the between-school component of variance could be used to modify sample sizes required of states that currently qualify for the exemptions from State NAEP minimum sample requirements. It also examined ways to preserve the infinite population assumptions for hypothesis testing related to comparisons between domain means. For this exploration, researchers developed hypothetical school and student population structures and hypothetical variance component distributions. For each variance component distribution, they determined the effective sample size resulting from the minimum state NAEP sample size requirements when the infinite population assumptions are a good approximation to reality. Results lend support to alternate sample size specifications both in states with few schools and in states with many small schools. The paper notes that permitting states to use design options other than the current State NAEP requirement could reduce costs related to test administration, scoring, and data processing. (Contains 10 tables.) (SLD)