This paper concerns the simplification of composite parametric surface meshes which conform to the boundary of each constituting patch. The goal is to eliminate the small edges which result from this boundary patch preserving constraint, provided that these small edges belong to an almost flat area. To this end, two tolerance areas with respect to the initial reference mesh are introduced to keep close to the surface. The reference mesh is then simplified and optimized (in terms of shape quality) so that the resulting mesh belongs to these tolerance areas. Several examples of surface meshes are provided in order to assess the efficiency of the simplification method.