The Internet is susceptible to congestion due to progressively increasing traffic as well as short-lived traffic surges. Traditional mechanisms to counter these effects over-provision the IP network to a significant degree. At the same time, the advent of dynamic circuits in L2/L1 networks has fueled the research in the area of network engineering which deals with the ability to add capacity in the higher layer (IP) by establishing dynamic circuits in the lower layers. However, effective usage of dynamic circuits is a challenge, as they can lead to IP routing instabilities. We present an approach wherein IP bypass links are established using dynamic circuits to alleviate congestion while keeping the routing stable in the IP layer. Proposed is an ILP based approach which computes the optimal set of circuits with and without the knowledge of the traffic matrix in the IP layer. The results show that even without the knowledge of the traffic matrix, the proposed method computes only a marginally higher number of bypasses, albeit at a higher capacity.