Processing data communications events by awakening threads in parallel active messaging interface of a parallel computer

Processing data communications events in a parallel active messaging interface (‘PAMI’) of a parallel computer that includes compute nodes that execute a parallel application, with the PAMI including data communications endpoints, and the endpoints are coupled for data communications through the PAMI and through other data communications resources, including determining by an advance function that there are no actionable data communications events pending for its context, placing by the advance function its thread of execution into a wait state, waiting for a subsequent data communications event for the context; responsive to occurrence of a subsequent data communications event for the context, awakening by the thread from the wait state; and processing by the advance function the subsequent data communications event now pending for the context.