The use of Gaussian Mixture Models (GMM), adapted through the Expectation Minimization(EM)algorithm, is not rare in Audio Analysis for Surveillance Applications and Environmental sound recognition. Their use, at a first glance, is founded on the good qualities of GMM models when aimed at approximating Probability Density Functions(PDF) of random variables. But in some cases, where models are to be adapted from small sample sets of specific and locally recorded signals, instead of large but generic databases, a problem of balance between model complexity and sample size may play an important role. From this perspective, we show, through simple sound classification experiments, that constrained GMM, with fewer degrees of freedom, as compared to GMM with full covariance matrices, provide better classification performances. Moreover, pushing this argument even further, we also show that a Parzen model (seen here as an over-constrained GMM) can do even better than usual GMM, in terms of classification error ratio