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This concise paper describes a new technique for upper bounding the performance of coherent binary phase-shift keyed (PSK) systems which derive a phase reference using one-shot maximum likelihood phase estimates. By performance, we mean any positive monotonically increasing function of phase error, such as error probability or power loss. A tight upper bound to the phase error cumulative distribution is shown to consist of the concave support to a previously derived Chernov bound. Performance measures appropriate for binary PSK systems are listed and evaluated with the new bound.