The multi-source Weber problem requires locating m new facilities in continuous space in order to minimize a sum of transportation costs to n fixed points or customers with known demands. Several heuristic methods have been developed to solve this problem. Typically, these algorithms move in descent directions from a specified starting solution until a local minimum is reached. In this paper, we consider the original heuristic proposed by Cooper (1963, 1964, 1972), which has no inherent neighbourhood structure. We show how a neighbourhood structure can be defined as in the H-heuristics of Love and Juel (1982) and either a pure descent or combined descent-ascent procedure employed to enhance the Cooper algorithm. Computational results are reported for the new hybrid algorithm.