Triangle strips are widely used as a method to accelerate the visualisation process of polygon models in interactive graphics applications. Another widely used method to improve drawing speed is the utilisation of multiresolution models. These models are constructed based on simplification algorithms. None of the current algorithms for searching strips contemplates the posterior simplification of the initial model. In this paper an algorithm for searching strips is presented. The triangles forming a strip are selected based on a simplification criterion according to the average quadratic error associated with the contraction of edges so that the model is simplified. In this manner the strips encountered are conserved as the model is being simplified. The strips generated in this way may be used to draw the polygon model in an incremental form or to transmit it progressively within a computer network.