Let G = (V, E) be a simple undirected graph with a set V of vertices and a set E of edges. Each vertex v E V has a demand d(V) epsilon Z(+) and a cost c(v) epsilon R+, where Z(+) and R+ denote the set of nonnegative integers and the set of nonnegative reals, respectively. The source location problem with vertex-connectivity requirements in a given graph G requires finding a set S of vertices minimizing Sigma(v epsilon S) c(v) such that there are at least d(v) pairwise vertex-disjoint paths from S to v for each vertex v epsilon V - S. It is known that if there exists a vertex v epsilon V with d(v) >= 4, then the problem is NP-hard even in the case where every vertex has a uniform cost. In this paper, we show that the problem can be solved in O(vertical bar V vertical bar(4) log(2) vertical bar V vertical bar) time if d(v) <= 3 holds for each vertex v epsilon V. (c) 2006 Elsevier B.V. All rights reserved.