As bit error rates decrease, the time required to measure a bit error rate (BER) or perform a BER test (i.e., to determine that a particular communications device's BER is less than some acceptable limit) increases dramatically. One cause of long measurement times is the difficulty of deciding a priori how many bits to measure to establish the BER to within a predetermined confidence interval width. This paper explores a new approach to deciding how many bits to measure, namely a sequential Bayesian approach. As measurement proceeds, the posterior distribution of BER is checked to see if the conclusion can be made that the BER rate is known to be within the desired range with high enough probability. Desired properties of the posterior distribution such as the maximum a postiori estimate and confidence limits can be computed quickly using off-the-shelf numerical software. Examples are given of using this method on bit error data measured with an Agilent 81250 parallel BER tester.