  We 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.
