spectra, guaranteed to yield a value for [$E_{\rm peak}$]{} as long as $\alpha > -2$. With three shape parameters, the Band function is flexible enough to stand in for a number of physical processes likely to occur in GRBs, including blackbody emission, synchrotron emission by thermal or power law electrons, as well as Compton scattering in any of its various guises. However, the Band function has a specific constant curvature that does not match any of these in detail, especially in the region where the two power law segments join (e.g.: see figure 8 in @burgess14).

For the purposes of the current work, it is more convenient to use a cut-off model power-law (the so-called COMP function in the spectral fitting package RMFIT[^1]), which is identical to the Band function in the limit $\beta \rightarrow -\infty$. The COMP functional form can also be cast in terms of [$E_{\rm peak}$]{}, as shown in equation \[comp\]. $$f_{\rm COMP}(E) = A \left( \frac{E}{100 \; {\rm keV}}\right)^{\alpha} 
\exp \left(-\frac{E\; {(2+\alpha)}}{E_{\rm peak}}\right){\rm .} \label{comp} $$ There are several reasons that drive our choice of this function for the simulations described below. First, for most bursts where the spectral evolution can be determined as a function 