determine which spectra from our simulation have enough total counts to be usable for spectroscopy and which spectra may have to be added together (binned) with others in order to meet a preferred level of significance. In order to reduce the variance (especially important for low count spectral bins at higher energies), we start with a long background accumulation from actual burst data. Following our procedure for the BATSE and GBM spectroscopy catalogs [@KanekoCat; @GoldsteinCat; @GruberCat] we fit a low-order ($\le$ 4) polynomial to the temporal variations of the background and interpolate the fitted model during the burst interval. Usually, we select regions for background fitting both before and after the burst, to avoid the need to extrapolate the background model. Since the background is fit to a polynomial in time in each energy bin, the variance associated with each bin is governed by the Gaussian statistics of the background temporal model parameters (the fitted polynomial coefficients). This variance is recovered in our simulations by resampling the background counts from a normal distribution, given the background model error for that bin.

The resulting simulated pulse is remarkably simple, yet it reproduces a number of characteristics of observed single pulses. First 