It is well-known (I hope) to all users of XSPEC that the chi-squared statistic is not appropriate if there are small numbers of counts (< 25) in any bins in the spectrum.

The solution is to use the C statistic (Cash 1978 ApJ 228, 939) which assumes only that the counts in each bin follow the Poisson distribution. One drawback of this statistic is that any background must be explicitly modelled.

Building on the work of Wachter et al. (1979 ApJ 230, 274) we have derived and implemented a new statistic which works on data when there is a background spectrum. The basic trick is to use a background model with one parameter for each spectral bin and to solve analytically for these parameter values.

With this new statistic it is no longer necessary to use the dangerous technique of grouping together spectral bins till the combined counts are in the Gaussian regime and chi-squared can be used.