  The incorporation of systematic uncertainties into confidence interval
calculations has been addressed recently in a paper by Conrad et al. (Physical
Review D 67 (2003) 012002). In their work, systematic uncertainities in
detector efficiencies and background flux predictions were incorporated
following the hybrid frequentist-Bayesian prescription of Cousins and Highland,
but using the likelihood ratio ordering of Feldman and Cousins in order to
produce "unified" confidence intervals. In general, the resulting intervals
behaved as one would intuitively expect, i.e. increased with increasing
uncertainties. However, it was noted that for numbers of observed events less
than or of order of the expected background, the intervals could sometimes
behave in a completely counter-intuitive fashion -- being seen to initially
decrease in the face of increasing uncertainties, but only for the case of
increasing signal efficiency uncertainty. In this comment, we show that the
problematic behaviour is due to integration over the signal efficiency
uncertainty while maximising the best fit alternative hypothesis likelihood. If
the alternative hypothesis likelihood is determined by unconditionally
maximising with respect to both the unknown signal and signal efficiency
uncertainty, the limits display the correct intuitive behaviour.
