The effectiveness of fine-needle aspiration (FNA) increases with the number of needle passes, but needle passes are also associated with increased risk of adverse events. The trade-off between needle passes and adequacy has not been well characterized. Clinical studies are limited because of their inherent variability and limited sample size. We developed mathematical models to compare the performance of a variety of sampling protocols under a wide range of conditions. Specifically, we compared the performance of sampling methods using a fixed number of needle passes with sampling methods using a rapid onsite evaluation (ROSE) with a variable number of needle passes. Variable sampling with ROSE generally required fewer needle passes than fixed sample size policies to achieve a desired adequacy rate. Variable sampling policies using ROSE achieve greater per-case adequacy with fewer needle passes than sampling policies using a fixed number of passes if assessor accuracy is high.