A network interface adapter includes a network interface and a client interface, for coupling to a client device so as to receive from the client device work requests to send messages over the network using a plurality of transport service instances. Message processing circuitry, coupled between the network interface and the client interface, includes an execution unit, which generates the messages in response to the work requests and passes the messages to the network interface to be sent over the network. A memory stores records of the messages that have been generated by the execution unit in respective lists according to the transport service instances with which the messages are associated. A completion unit receives the records from the memory and, responsive thereto, reports to the client device upon completion of the messages.