In the single-source unsplittable flow problem we are given a graph G, a source vertex s and a set of sinks t/sub 1/, ..., t/sub k/ with associated demands. We seek a single s-t/sub i/ flow path for each commodity i so that the demands are satisfied and the total flow routed across any edge e is bounded by its capacity c/sub e/. The problem is an NP-hard variant of max flow and a generalization of single-source edge-disjoint paths with applications to scheduling, load balancing and virtual-circuit routing problems. In a significant development, Kleinberg gave recently constant-factor approximation algorithms for several natural optimization versions of the problem. In this paper we give a generic framework, that yields simpler algorithms and significant improvements upon the constant factors. Our framework, with appropriate subroutines applies to all optimization versions previously considered and treats in a unified manner directed and undirected graphs.