An investigation of the ground state of the classical Heisenberg exchange energy in spinels has led toseveral new results. By means of a recent generalization of the method of Luttinger and Tisza, we haverigorously obtained the ground state in part of the exchange parameter space defined by nearest neighborABandBBinteractions for tetragonally distorted spinels. The regions in this space where the Ne´el andYafet-Kittel configurations minimize the energy are much smaller than predicted by the Yafet-Kittel six-sublatticetheory. Outside of these regions, there exists a domain where the ground state is an antiferromagneticspiral similar to those recently introduced in the literature. In still other regions, the ground stateis a new type of spiral which is ferrimagnetic. An investigation of a parameter region including cubic spinelsshows that such a ferrimagnetic spiral yields an appreciably lower energy than that given by the Yafet-Kittelmodel and is locally stable up to a specified ratio ofBBtoABinteractions. The generalized Luttinger-Tiszamethod shows it to be the best possible ferrimagnetic spiral up to and beyond the point of instability, butfails to prove it to be the ground state. An examination of small deviations at the point of instability indicatesthe existence of spin configurations much more complex than the magnetic spirals proposed here.