2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/83477We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson distributed variate where the mean is the sum of a known background and an unknown non-negative signal. We point out that the intervals do not have coverage in the usual sense but can be made to have such with a modification that does not affect the believability and other desirable features of this attractive construction. A similar modification can be used to provide coverage to the construction recently proposed by Cousins for the Gaussian-with-boundary problem.9 pages, 2 figuresData Analysis, Statistics and ProbabilityGeneral Physicstext