Assuming bit errors are independently distributed with a constant probability of error pe, it is shown that a simple estimator is highly efficient for estimation of pe. The estimator is based on a simple function of the number of sync words containing no bit errors. The estimator is shown to be maximum likelihood, minimum chi-square, and modified minimum chi-square when the quality index reported is simply the percent of frames containing zero errors. An approximate confidence interval for peis obtained, and a determination of the number of sync words to observe in order to obtain an approximate confidence interval of fixed length is indicated. The method of scoring which can be used to obtain a more efficient estimator of peis described.