The inadequacy of a single-charge isotropic description of the renormalization group (RG) behavior is demonstrated for 2-dimensional nonlinear sigma-models on real Stiefel manifolds. The RG equations governing the evolution of the homothety charge t and the anisotropy magnitude η are obtained and an explicit formula for the RG trajectories in the η, t plane is derived. The existence of asymptotic freedom (AF) and its intensity are shown to depend on the value of η.