In this paper we propose a discriminative approach to acoustic space dimensionality selection based on maximum entropy modelling. We form a set of constraints by composing the acoustic space with the space of phone classes, and use a continuous feature formulation of maximum entropy modelling to select an optimal feature set. The suggested approach has two steps: (1) the selection of the best acoustic space that efficiently and economically represents the acoustic data and its variability; (2) the combination of selected acoustic features in the maximum entropy frameworkto estimate the posterior probabilities over the phonetic labels given the acoustic input. Specific contributions of this paper include a parameter estimation algorithm (generalized improved iterative scaling) that enables the use of negative features, the parameterization of constraint functions using Gaussian mixture models, and experimental results using the TIMIT database.