The integrated design of telecommunication networks with multiple layers, representing different technologies like IP, SDH and WDM, has become a topic of high interest in recent years, due to the potential savings compared to single-layer network design. In this talk, we study a two-layer network design problem with the possiblities to install logical links at different bitrates. We formulate the problem as an integer linear program and develop a branch-and-cut approach. For this, we translate cutting planes for the single layer network design problem to our setting, in particular, cut-set inequalities and general flow-cut-set inequalities. Computational experiments show the good performance of these cutting planes in the multi-layer setting and emphasize the differences with single layer network design. This is a joint work with Sebastian Orlowski, Christian Raack (both Zuse Institute Berlin), Thomas Engel, and Georg Baier (Nokia Siemens Networks, Munich).