An investigation of the ground state of the classical Heisenberg exchange energy in spinels has led to several new results. By means of a recent generalization of the method of Luttinger and Tisza, we have rigorously obtained the ground state in part of the exchange parameter space defined by nearest neighbor AB and BB interactions for tetragonally distorted spinels. The regions in this space where the Néel and Yafet-Kittel configurations minimize the energy are much smaller than predicted by the Yafet-Kittel six-sublattice theory. Outside of these regions, there exists a domain where the ground state is an antiferromagnetic spiral 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 spinels shows that such a ferrimagnetic spiral yields an appreciably lower energy than that given by the Yafet-Kittel model and is locally stable up to a specified ratio of BB to AB interactions. The generalized Luttinger-Tisza method shows it to be the best possible ferrimagnetic spiral up to and beyond the point of instability, but fails to prove it to be the ground state. An examination of small deviations at the point of instability indicates the existence of spin configurations much more complex than the magnetic spirals proposed here.