Verhelst derived a solution for a constrained regression problem which occurs in the interval measurement application of ALSCAL and related MDS-algorithms. In the present paper it is shown that Verhelst's solution is based on an implicit nonsingularity assumption. A general solution, which contains Verhelst's solution as a special case, is derived by a simple completing-the-squares type approach instead of partial differentiation with a Lagrange multiplier. In addition, this approach permits the identification of a small interval which uniquely contains the optimal value of a parameter needed to solve the special case where Verhelst's solution is valid.