Weber's problem consists in locating a facility in the plane in such a way that the weighted sum of Euclidean distances to n given points be minimum. The case where some weights are positive and some are negative is shown to be a d.-c. program, reducible to a problem of concave minimization over a convex set. The latter is solved by outer-approximation and vertex enumeration. Moreover, locational constraints can be taken into account by combining the previous algorithm with an enumerative procedure on the set of feasible regions. Computational experience with n up to 1000 is reported on.