We present an improvement (the backward trimming procedure) over our algorithm for 3D numerical integration of molecular integrals [J. M. Perez-Jorda, A, D. Becke, and E. San-Fabian, J. Chem. Phys. 100, 6520 (1994), the standard procedure]. Tests with 21 molecules indicate that the backward trimming procedure gives errors similar to those obtained with the standard procedure, but;; with a five fold reduction in the number of grid points.