  The method of obtaining confidence intervals on a subset of the total number
of parameters (p) of a model used for fitting X-ray spectra is to perturb the
best-fitting model until, for each parameter, a range is found for which the
change in the fit statistic is equal to some critical value. This critical
value corresponds to the desired confidence level and is obtained from the
chi-square distribution for q degrees of freedom, where q is the number of
interesting parameters. With the advent of better energy-resolution detectors,
such as those onboard ASCA it has become more common to fit complex models with
narrow features, comparable to the instrumental energy resolution. To
investigate whether this leads to significant non-Gaussian deviations between
data and model, we use simulations based on ASCA data and we show that the
method is still valid in such cases. We also investigate the weak-source limit
as well as the case of obtaining upper limits on equivalents widths of weak
emission lines and find that for all practical purposes the method gives the
correct confidence ranges. However, upper limits on emission-line equivalent
widths may be over-estimated in the extreme Poisson limit.
