Moment methods for analyzing repeated binary responses have been proposed by Liang and Zeger (1986, Biometrika 73, 13-22), and extended by Prentice (1988, Biometrics 44, 1033-1048). In their generalized estimating equations (GEE), both Liang and Zeger (1986) and Prentice (1988) estimate the parameters associated with the expected value of an individual's vector of binary responses as well as the correlations between pairs of binary responses. In this paper, we discuss one-step estimators, i.e., estimators obtained from one step of the generalized estimating equations, and compare their performance to that of the fully iterated estimators in small samples. In simulations, we find the performance of the one-step estimator to be qualitatively similar to that of the fully iterated estimator. When the sample size is small and the association between binary responses is high, we recommend using the one-step estimator to circumvent convergence problems associated with the fully iterated GEE algorithm. Furthermore, we find the GEE methods to be more efficient than ordinary logistic regression with variance correction for estimating the effect of a time-varying covariate.