Routing policies determined by Internet Service Providers (ISPs) can create sub-optimal communication paths in terms of Quality of Service (QoS). An Overlay Network (ON) architecture enables the definition of custom routing policies between Points of Presence, enabling QoS metrics improvement for a particular application. This work proposes a forwarding strategy to implement a tunnelless overlay architecture, enabling different traffic flows to follow different paths in order to provide different QoS metrics for each one. Besides, the solution does not affect the packets MTU and can be deployed independently of the underlying ISPs. This article introduces a system architecture built over the software-defined networking paradigm, taking advantage of the centralized view of the network resources and the ability to face challenges by deploying applications at the controller level. The main components of the forwarding strategy have been designed, implemented and tested over both an emulated and a real network to demonstrate its feasibility.