Finney proposed the use of a fiducial interval for the median response dose based on Fieller's theorem. An alternative is to use the asymptotic confidence interval. The simulations by Abdelbasit and Plackett suggest that the two intervals have similar coverage probabilities. We compare the two intervals theoretically and in an expanded simulation study. Our results show that Fieller intervals are generally superior. An attempt is made to characterize how and when the two intervals differ.