The mixture of inverse covariances model is a low-complexity, approximate decomposition of the inverse covariance matrices in a Gaussian mixture model which achieves high modeling accuracy with very good computational efficiency. In this model, the inverse covariances are decomposed into a linear combination of K shared prototype matrices. In this paper, we introduce an extension of this model which uses a variable number of prototypes per Gaussian for improved efficiency. The number of prototypes per Gaussian is optimized using a maximum likelihood criterion. This variable length model is shown to achieve significantly better accuracy at a given complexity level on several speech recognition tasks.