  When searching for new physics effects, collaborations will often wish to
publish upper limits and intervals with a lower confidence level than the
threshold they would set to claim an excess or a discovery. However, confidence
intervals are typically constructed to provide constant coverage, or
probability to contain the true value, with possible overcoverage if the random
parameter is discrete. In particular, that means that the confidence interval
will contain the $0$-signal case with the same frequency as the confidence
level. This paper details a modification to the Feldman-Cousins method to allow
a different, higher excess reporting significance than the interval confidence
level.
