The hyperfine structure of several paramagnetic ions and atoms such as Mn++ is known to contain an unexpected and large contribution due to some admixture of unpaired s electrons in the wave function. An explanation of this is proposed in terms of the effect of exchange with the 3d electrons on the 2s and 3s electrons. Since the spins of the 3d electrons are at least partially lined up, exchange affects 2s, 3s electrons with parallel and antiparallel spin differently, so that the 2s2 3s2 electrons are not exactly paired. A rough preliminary calculation gives sufficiently good agreement with experiment to suggest that the proposed mechanism is an important factor, if not the complete explanation. Some detailed differences between various ions remain puzzling.