In most wireless communications research, the channel models considered experience less severe fading than the classic Rayleigh fading case. In this work, however, we investigate MIMO channels where the fading is more severe. In these environments, we show that the coefficient of variation of the channel amplitudes is a good predictor of the link mutual information, for a variety of models. We propose a novel channel model for severely fading channels based on the complex multivariate t distribution. For this model, we are able to compute exact results for the ergodic mutual information and approximations to the outage probabilities for the mutual information. Applications of this work include wireless sensors, RF tagging, land-mobile, indoor-mobile, ground-penetrating radar, and ionospheric radio links. Finally, we point out that the methodology can also be extended to evaluate the mutual information of a cellular MIMO link and the performance of various MIMO receivers in a cellular scenario. In these cellular applications, the channel itself is not severely fading but the multivariate t distribution can be applied to model the effects of inter-cell interference.