Aspects of the invention pertain to transmitting packet data across a computer network. The packets may be sent via one or more distinct routes from a source to a destination. Each route may employ multiple routers disposed along the network. Non-colliding routes are determined by transmitting pairs of probe packets along the routes. A first probe packet has a maximal length, and a second probe packet has a minimal length. Depending on the order of arrival of the probe packets, the system determines whether two transport layer ports at the destination device collide. If there is a collision, then the system searches for a set of non-colliding ports. Once the non-colliding ports are determined, application data may be sent as packets along the different routes to those ports.