A vector quantisation codebook can be modelled as a set of probability density functions. The problem of estimating the parameters determining mixture probability density models can be solved using a log-likelihood based re-estimation procedure. On the other hand, this problem can be also viewed as a conventional optimisation problem. Consequently, gradient descent techniques may be used to obtain values of the model parameters. The main advantage of these techniques over the re-estimation procedure is higher robustness due to an initial estimation of the model parameters. In the paper, we describe a descent algorithm along with a criterion function, we propose. We obtained some promising results by applying this algorithm to one and two-variate pseudo Gaussian mixture probability density functions and further to signal vectors of a continuous speech database.