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This paper presents an adaptive message logging algorithm that keeps time and space costs low by logging only a fraction of the messages. The algorithm dynamically tracks dependences among messages to determine which cause domino effects and must be traced. The domino effect can force a replay to start arbitrarily far back in the execution, and domino-free replay allows any part of the execution to be quickly reexecuted. Experiments on an iPSC/860 hypercube indicate that our algorithm logs only 1-10% of the messages, a one to two order of magnitude reduction over past schemes which log every message. The experiments also show that the resulting logs provide a small bound on the amount of reexecution needed to satisfy any replay request. The new logging algorithm thus reduces the overhead of message logging while bounding the response time to replay requests.