In this article, we document a new implementation of the fuzzy cells scheme for numerical integration in polyatomic systems [Becke, J. Chem. Phys. 1998, 88, 2547] and compare its efficiency and accuracy with respect to an integration scheme based on the Voronoi space partitioning. We show that the accuracy of both methods is comparable, but that the fuzzy cells scheme is better suited for geometry optimization. For this method, we also introduce the locally dense grid concept and present a proof-of-concept application. © 2013 Wiley Periodicals, Inc.