According to another embodiment of the invention, TWAMP path discovery is performed to determine a sequence of IP addresses of a forward direction TWAMP E2E path to be traversed by two different TWAMP test sessions between a Sender and a Reflector. Then, additional TWAMP test request packets are transmitted for the different TWAMP test sessions; and TWAMP test reply messages are received responsive to respective ones of the TWAMP test request packets. Responsive to the TWAMP test reply messages, a PM is determined that is specific to the different sequences of IP addresses of the forward direction TWAMP E2E paths traversed by the two different TWAMP test sessions.