In the 1970s and 1980s, the National Assessment of Educational Progress (NAEP) built a longitudinal record as the Nation's Report Card based on periodic brief assessments of a modest but representative sample of the nation's students. In 1990, data collection was expanded from a sample of 10,000 students in each grade and subject area to 100,000 to provide the basis for state-by-state comparisons. This expansion brought about an large increase in data collection costs. There is a frustrating conflict between the need for precise estimates of educational achievement and the cost of obtaining these estimates. This study considers using state assessments to supplement, or reduce, NAEP samples. The relationships between using state assessment scores and reducing sample size are demonstrated mathematically. Implementing this approach would require step-by-step planning and implementation. While the linkage of student-level assessment scores would be ideal, linkages based on school-level summary statistics appear to be sufficient when the correlations between tests is high. Many states appear to have tests with such correlations to the NAEP. The cost of linking procedures required for implementing the sample size reductions is in the range of $5,000 to $10,000 per state, which is a small percentage of the cost of the administration of State NAEP in an additional 50 schools in the state. Many states have difficulty recruiting schools for the NAEP and would welcome this initiative. These analyses suggest that several states could be involved in sample size reduction, possibly as early as 1998. (Contains one table and one figure.) (SLD)