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Checkpointing is a very effective technique to ensure the continuity of long running applications in the occurrence of failures. However, one of the handicaps of coordinated checkpointing is the high latency for committing output from the application to the external world. Enhancing the checkpointing scheme, with a message logging protocol is a good solution to reduce the output latency. The idea is to track the sources of non-determinism in order to replay the application in a reproducible way during rollback recovery. We present a new event logging scheme that only logs those messages that may be delivered non deterministically to the application. While other schemes keep track of the arrival order of all the messages we just save the delivery order of some of them. Our scheme exploits the semantics of message passing and is able to reduce considerably the number of receiving events when compared with other existing schemes. We present some performance results that compare the output latency of coordinated checkpointing, pessimistic message logging, optimistic message logging and our event logging scheme.