Telecommunication networks are generally dimensioned to provide services with small delays and high throughput during peak-periods. Due to the sizable difference in the network utilization between the peak and off-peak periods as well as the requirements of robust performance in face of both traffic burstiness and various types of network failures, these networks are significantly over-dimensioned for the average network loads. In this paper, we propose to use this extra capacity for supporting a deferrable traffic class with some guarantees on its end-to-end delays. Using the Software-Defined Networking (SDN) capabilities for controlling the network ingress rates of the deferrable traffic class in real time, we ensure that such a service would remain transparent to existing delay-sensitive traffic. To estimate the available capacities for the deferrable service, we analyze large deviations for the proposed traffic model. Starting from an initial network designed for delay-sensitive traffic, one can readily "overlay" a new network for the deferrable service at no extra cost. This overlaid network has the same topology as the original one, and its link capacities can be directly computed from the characteristics of the existing traffic, the original link capacities, and the end-to-end delay tolerances.