A telecommunication system and a method for generating a real time connection between a first endpoint and a second endpoint in an IP network using an ICE STUN connectivity check follow a procedure that includes the steps of generating a list of possible connection paths between the first endpoint and the second endpoint, establishing a respective priority for each possible connection path included in the list, and generating the real time connection between the first endpoint and the second endpoint. During this procedure first there is an attempt to generate the real time connection using the highest-priority connection path. If this is not possible, then the system attempts to establish the real connection using the connection path with the next highest priority, until the real time connection is actually established. Furthermore, for each possible connection path, its respective quality-of-service value is determined and is considered when establishing its priority on the list.