This paper describes computational methods for applying known theoretical results to obtain confidence bounds for a single location or scale parameter from quantal data using the discrete distribution of either the maximum likelihood or a method of moments estimator.For some standard dose-response models an algorithm which makes finding such bounds computationally feasible is described.Also described are more easily computed approximate confidence bounds based on the asymptotic distribution of the point estimators.Computational studies indicate that these methods can also be applied to the more practical problem of finding confidence bounds for location after estimating an unknown scale parameter.