WAN provider links are often operated at low utilization levels, which leaves large unused capacity (headroom). In this paper, we propose using Software Defined Networking (SDN) controllers to support novel Static Headroom (SH) and Dynamic Headroom (DH) services to allow customers to fill this headroom with Elephant Flows (EFs) without adversely affecting the provider's ability to meet its Best-Effort (BE) service-level agreements, and ability to absorb extra traffic load created during failure recovery periods. Our solution calls for the use of lower-priority service for EFs. We use simulations to compare SH service with BE service, and DH service with SH service. When EFs are sent on BE service, they could cause packet losses in general-purpose IP traffic, especially when the burstiness of the latter is high, while with SH service, this packet loss rate is reduced to 0. While DH service requires the added complexity of a provider SDN controller, the ability to dynamically route EFs on lower-utilized links results in higher average EF throughput. The higher the non-uniformity (from a node-pair perspective) in network traffic, the greater the DH gain factor.