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This paper presents the sensitivity penalty for burst-mode receivers using avalanche photodiodes. The analysis takes into account detailed avalanche photodiode statistics, additive Gaussian noise, intersymbol interference and dc offsets in the receiver channel. The penalty has been calculated via comparison of bit-error rates (BERs), obtained using numerical integration, both in continuous- and burst-mode operation. Sensitivity penalties for burst-mode operation as a function of the mean avalanche gain are presented. The Gaussian approximation systematically underestimates the burst-mode penalty. It is shown that the penalty depends upon both the type of avalanche photodiode (APD) and the required BER. Optimum avalanche gains maximizing the sensitivity of the receiver are given. The influence of dc-offsets upon the sensitivity is studied. Furthermore, it is shown that the impulse response of the filters used to extract the decision threshold profoundly impacts the receiver performance. Finally, some important guidelines for the design of high sensitivity and wide dynamic range burst-mode receivers are given.