  Brion proved that the valuation cone of a complex spherical variety is a
fundamental domain for a finite reflection group, called the little Weyl group.
The principal goal of this paper is to generalize this fundamental theorem to
fields of characteristic unequal to 2. We also prove a weaker version which
holds in characteristic 2, as well. Our main tool is a generalization of
Akhiezer's classification of spherical rank-1-varieties.
