Three methods of obtaining confidence intervals for the risk ratio offailure in two independent binomial samples are compared. The three are (A) the method of Thomas and Gart (1977), (B) an adaptation of the method of Fieller using the normal distribution, and (C) a proposed method using a logarithmic transformation. On the basis of extensive simulations we have concluded that Method A is reasonable but conservative, Method B is erratic and should not be used, aszd Method C is reasonable and less conservative than Method A. Method C, cotnputationally the simplest, is recommended.