Probabilistic shaping of quadrature amplitude modulation (QAM) is used to enhance the sensitivity of an optical communication system. Sensitivity gains of 0.43 and 0.8 dB are demonstrated in back-to-back experiments by the shaping of 16QAM and 64QAM, respectively. Furthermore, numerical simulations are used to prove the robustness of probabilistic shaping to a mismatch between the constellation used and the signal-to-noise ratio (SNR) of the channel. It is found that, accepting a 0.1-dB SNR penalty, only four shaping distributions are required to support these gains for 64QAM.