Let be a collection of independent, identically distributed Poisson θ random variables. Confidence intervals for θ can be constructed by the Wald method, by exact inference, from a variance stabilizing transformation, or by many other techniques. When nθ is small, actual and nominal coverage can differ substantially. We compare nine confidence intervals for a Poisson mean with respect to coverage and expected width of confidence limits. We show that, for small nθ: of the confidence intervals considered, only the exact interval maintains coverage probabilities; while the scores interval approximately maintains coverage probability, its expected width exceeds the exact interval's; and a modified version of the confidence interval based on the variance stabilized confidence interval has coverage properties near the nominal and an expected width that is not particularly large. Thus, we recommend that investigators desiring true cover not less than nominal use the exact interval and those willing to accept approximate coverage use a modified form of the variance stabilized interval.