Abstract : An appreciable number of magnetic materials with the spinel structure exhibit tetragonal symmetry, rather than cubic, in their x-ray diffraction patterns. Because of the distortion, five different nearest-neighbor exchange interactions are possible, so that four ratios (t, u, v, and w) amongst these interactions are required for the characterization of such a material. The generalized Luttinger-Tisza method (GLT) is used to determine rigorously the ranges of values of the above ratios (regions in t, u, v, w parameter space) for which the familiar Neel, Yafet-Kittel, and collinear antifenromagnetic spin configura tions (k0 modes) are the ground states of the classical Heisenberg exchange energy. The ground-state regions are found to be significant ly smaller than would be predicted on the basis of a sublattice model. Consequently, knowledge of the actual spin configuration can place impor tant restrictions upon the relative strengths of exchange interactions, as in the case of copper chromite. In addition, we find that the desta bilizing k vector is not always parallel to a symmetry direction, even for nearly-cubic spinels. (Author)