The Mobius transformations recently proposed for integrating functions with a sharp peak close to a single boundary of integration (H. H. H. Homeier and E. O. Steinborn, J. Comput. Phys. 87, 61, 1990) are used to extend Ruedenberg's algorithm for two-center exchange integrals to cases with very diffuse STOs. (C) 1994 John Wiley & Sons, Inc.