The stochastic transport of MeV ions induced by low‐nmagnetic perturbations is studied, focusing chiefly on the stochastic mechanism operative forpassingparticles inlow‐frequency perturbations. Beginning with a single‐harmonic form for the perturbing field, it is first shown numerically and analytically that the stochastic threshold of energetic particles can be substantially lower than that of the magnetic field, contrary to earlier expectations, so that magnetic perturbations could cause appreciable loss of energetic ions without destroying the bulk confinement. The analytic theory is then extended in a number of directions, to clarify the relation of the present stochastic mechanism to instances already found, to allow for more complex perturbations, and to consider the more general relationship between the stochasticity of magnetic fields and that of particles of differing energies (and pitch angles) moving in those fields. It is shown that the stochastic threshold is, in general, a nonmonotonic function of energy, whose form can to some extent be tailored to achieve desired goals (e.g., burn control or ash removal) by a judicious choice of the perturbation. Illustrative perturbations are exhibited that are stochastic for low‐ but not for high‐energy ions, for high‐ but not for low‐energy ions, and for intermediate‐energy ions, but not for low or high energy. The second possibility is the behavior needed for burn control; the third provides a possible mechanism for ash removal.