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A technique for improving the performance of an OSNR monitor based on a polarisation nulling method with the downhill simplex algorithm is demonstrated. Establishing a compromise between accuracy and acquisition time, the monitor has been calibrated to 0.72 dB/390 ms and 0.98 dB/320 ms, over a range of nearly 21 dB. As far as is known, these are the best values achieved with such an OSNR monitoring method.