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Even if nonlinear system identification tends to provide highly accurate models these last decades, the user still remains interested in finding the good balance between high accuracy models and moderate complexity. In this paper, both a dedicated neural network design and a model reduction approach are proposed in order to improve this balance. The proposed neural network design helps to reduce the number of parameters of the model after the training phase preserving the estimation accuracy of the non reduced model. Even if this reduction is achieved by a convenient choice of the activation functions and the initial conditions of the synaptic weights, it nevertheless leads to models among the most encountered in the literature assuring all the interest of such method. To validate the proposed approach, we identified the Wiener-Hammerstein benchmark nonlinear system proposed in SYSID2009 .