The effect of adiabaticity and superadiabaticity limitations on the use of radio-frequency-augmented magnetic-mirror confinement is examined. It is shown that the scaling of the region over which the r. f. fields are applied to maintain a given level of adiabaticity is such that, although the fields decrease as resonance is approached, the total r. f. energy stored in the resonance region remains constant. Assuming that the dissipation is proportional to the energy stored, we conclude that the external energy supplied is not reduced from the energy requirements of non-resonant r. f. containment. In fact, the weak additional scaling required to maintain containment by superadiabaticity implies that resonant r. f. containment requires more applied power. The stochastic heating, resulting from the small-phase uncorrelated energy changes occurring on each pass through resonance, when superadiabaticity is not satisfied, is such that only a small improvement in the field strength required for containment can be made by operating in this mode.