It has been shown that, when used for pattern recognition with supervised learning, a network with one hidden layer tends to the optimal Bayesian classifier provided that three parameters simultaneously tend to certain limiting values: the sample size and the number of cells in the hidden layer must both tend to infinity and some mean error function over the learning sample must tend to its absolute minimum. When at least one of the parameters is constant (in practice the size of the learning sample), then it is no longer justified mathematically to have the other two parameters tend to the values specified above in order to improve the solution. A lot of research has gone into determining the optimal value of the number of cells in the hidden layer. In this paper, we examine, in a more global manner, the joint determination of optimal values of the two free parameters: the number of hidden cells and the mean error. We exhibit an objective factor of problem complexity: the amount of overlap between classes in the representation space. Contrary to what is generally accepted, we show that networks usually regarded as oversized despite a learning phase of limited duration regularly yield better results than smaller networks designed to reach the absolute minimum of the square error during the learning phase. This phenomenon is all the more noticeable that class overlap is high. To control this latter factor, our experiments used an original pattern recognition problem generator, also described in this paper.