In Information Retrieval, test collections are usually built using the pooling method. Many pooling strategies have been developed for the pooling method. Herein, we address the question of identifying the best pooling strategy when evaluating systems using precision-oriented measures in presence of budget constraints on the number of documents to be evaluated. As a quality measurement we use the bias introduced by the pooling strategy, measured both in terms of Mean Absolute Error of the scores and in terms of ranking errors. Based on experiments on 15 test collections, we conclude that, for precision-oriented measures, the best strategies are based on Rank-Biased Precision (RBP). These results can inform collection builders because they suggest that, under fixed assessment budget constraints, RBP-based sampling produces less biased pools than other alternatives.