Statistical analysis using confidence intervals is now a preferred approach in the medical literature, and confidence limits for binomial proportions and Poisson counts are commonly required. Normal approximations of varying accuracy are often used in such situations and it is not generally realised that non-iterative exact solutions are available. This paper shows that the exact binomial and Poisson confidence limits can be expressed very simply in terms of the inverse beta and inverse gamma distributions, and describes two macros in the SAS programming language to perform the computations. The exact solutions are compared with some approximations and further applications of the techniques are described.