A method for passing messages in a parallel computer system constructed as a plurality of compute nodes interconnected as a network where each compute node includes a DMA engine but includes only a limited number of byte counters for tracking a number of bytes that are sent or received by the DMA engine, where the byte counters may be used in shared counter or exclusive counter modes of operation. The method includes using rendezvous protocol, a source compute node deterministically sending a request to send (RTS) message with a single RTS descriptor using an exclusive injection counter to track both the RTS message and message data to be sent in association with the RTS message, to a destination compute node such that the RTS descriptor indicates to the destination compute node that the message data will be adaptively routed to the destination node. Using one DMA FIFO at the source compute node, the RTS descriptors are maintained for rendezvous messages destined for the destination compute node to ensure proper message data ordering thereat. Using a reception counter at a DMA engine, the destination compute node tracks reception of the RTS and associated message data and sends a clear to send (CTS) message to the source node in a rendezvous protocol form of a remote get to accept the RTS message and message data and processing the remote get (CTS) by the source compute node DMA engine to provide the message data to be sent.