A network interface is disclosed for enabling remote programmed I/O to be carried out in a “lossy” network (one in which packets may be dropped). The network interface: (1) receives a plurality of memory transaction messages (MTM's); (2) determines that they are destined for a particular remote node; (3) determines a transaction type for each MTM; (4) composes, for each MTM, a network packet to encapsulate at least a portion of that MTM; (5) assigns a priority to each network packet based upon the transaction type of the MTM that it is encapsulating; (6) sends the network packets into a lossy network destined for the remote node; and (7) ensures that at least a subset of the network packets are received by the remote node in a proper sequence. By doing this, the network interface makes it possible to carry out remote programmed I/O, even across a lossy network.