We address the problem of learning the structure of Gaussian graphical models for use in automatic speech recognition, a means of controlling the form of the inverse covariance matrices of such systems. With particular focus on data sparsity issues, we implement a method for imposing graphical model structure on a Gaussian mixture system, using a convex optimisation technique to maximise a penalised likelihood expression. The results of initial experiments on a phone recognition task show a performance improvement over an equivalent full-covariance system.