In this paper, we propose a novel priority-aware solution named bypass to handle high- and low-priority traffic in multi-layer networks. Our approach assumes diversification of elastic optical spectrum to ensure additional resources reserved for emergency situations. When congestion occurs, the solution dynamically provides new paths, allocating a hidden spectrum to offload traffic from the congested links in the IP layer. Resources for a bypass are selected based on traffic priority. High-priority traffic always gets the shortest bypasses in terms of physical distance, which minimizes delay. Bypasses for low-priority traffic can be established if the utilization of the spectrum along the path is below the assumed threshold. The software-defined networking controller ensures the global view of the network and cooperation between IP and elastic optical layers. Simulation results show that the solution successfully reduces the amount of rejected high-priority traffic when compared to regular bypasses and when no bypasses are used. Also, overall bandwidth blocking probability is lower when our priority-aware bypasses are used.