Alterations in speech motor control in depressed individuals have been found to manifest as a reduction in spectral variability. In this paper we present a novel method for measuring acoustic volume — a model-based measure that is reflective of this decrease in spectral variability — and assess the ability of features resulting from this measure for indexing a speaker's level of depression. A Monte Carlo approximation that enables the computation of this measure is also outlined in this paper. Results found using the AVEC 2013 Challenge Dataset indicate there is a statistically significant reduction in acoustic variation with increasing levels of speaker depression, and using features designed to capture this change it is possible to outperform a range of conventional spectral measures when predicting a speaker's level of depression.