We thank Professor Yasutaka Chiba [1] for commenting on Rigdon and Hudgens (RH) [2]. Chiba [1] described a certain exact confidence interval reported in RH as “somewhat unnatural.” Chiba also presented an alternative approach to constructing confidence intervals [3]. In this response, we (i) provide a simple explanation why the confidence interval in RH appeared “unnatural,” and (ii) explain the relationship between the RH [2] and Chiba [3] confidence intervals. Essentially the two approaches are equivalent, except RH entails inverting one two-sided test whereas Chiba inverts two one-sided tests. We present a more computationally efficient method (RLH) for computing the RH intervals based on Chiba’s principal stratification formulation of the problem. We also propose a third method based on Blaker [4] which inverts a single two-sided test but forms a confidence interval that is at least as narrow as inverting two one-sided tests. Simulation results show the RLH intervals tend to be as narrow or narrower than the Chiba and Blaker intervals on average.