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The bit error rate of a binary phase shift keying (BPSK) signal in Ricean-faded cochannel interference is studied. A precise bit error rate expression is derived for a bandlimited BPSK signal corrupted by an arbitrary number of asynchronous Ricean-faded interfering signals. An error rate estimation based on a saddlepoint approximation is also provided. It is shown that this approximation is highly accurate. For the special case, when there is one synchronous Ricean-faded interfering signal in an interference-limited environment, an asymptotic error rate analysis based on the saddle point approximation reveals that fading in the cochannel interfering signal can have different impacts on the desired user's error rate performance. Our study shows that when the signal-to-interference ratio (SIR) is sufficiently large, the error floor of the desired user signal decreases with an increase of the Rice factor in the interfering user's fading channel. However, the opposite phenomenon can happen when the SIR is small.