We present re-estimation formulae for semi-tied covariance (STC) transformation matrices based on a maximum mutual information (MMI) criterion. These re-estimation formulae are different from those that have appeared previously in the literature. Moreover, we present a positive definiteness criterion with which the regularization constant present in all NMI re-estimation formulae can be reliably set to provide both consistent improvements in the total mutual information of the training set, as well as fast convergence. We combine the STC re-estimation formulae with their like for speaker-independent means and variances, and update all parameters during NMI speaker adapted training (MMI-SAT). We present the results of two sets of speech recognition experiments conducted on the the 1998 Broadcast News evaluation set, as well as a corpus of meeting room data collected at the Interactive Systems Laboratories of the Carnegie Mellon University.