In this paper we present a novel approach for estimating feature-space maximum likelihood linear regression (fMLLR) transforms for full-covariance Gaussian models by directly maximizing the likelihood function by repeated line search in the direction of the gradient. We do this in a pre-transformed parameter space such that an approximation to the expected Hessian is proportional to the unit matrix. The proposed algorithm is as efficient or more efficient than standard approaches, and is more flexible because it can naturally be combined with sets of basis transforms and with full covariance and subspace precision and mean (SPAM) models.