We formulate direct, neutrino flavor-changing interactions in a framework that fits smoothly with the parametrization of two- and three-state mixing of massive neutrino states. We show that even small direct interaction strengths could have important consequences on the interpretation of currently running and proposed oscillation experiments. The oscillation amplitude and the borders of the allowed regions in two- and three-flavor mixing parameter space can be sensitive to the presence of direct interactions when the transition probability is small. We use extensively the high sensitivity of the NOMAD experiment to illustrate potentially large effects from small, direct flavor violation. In the purely leptonic sector, we find that the clean (Formula presented) and (Formula presented) beams from a (Formula presented) collider could provide the sharpest tests of direct flavor violation. © 2000 The American Physical Society.