and @lu10 have both suggested that the tracking behavior may arise when several pulses are run together, so that they many not be clearly distinguished. We will also address this below. In many cases, the rising portion may be too short, compared with the decay, to be able to determine any trend in [$E_{\rm peak}$]{}; this is common with weaker events, especially if there is only a single spectrum in the rising portion before the peak that is significant enough to obtain a fit. We take this as a motivation for our hypothesis: that signal-to-noise sampling under-emphasizes the lowest and highest energies, which are found preferentially on the rise and decay portions of pulses (true for both HTS and HIT pulses), resulting in the observed narrow distributions.

In this section, we will concentrate on bright, single pulses with HTS behavior. There is ample motivation for this: several very bright bursts are either composed of single pulses or have at least one well-separated pulse with clear HTS evolution. In several of these cases, the temporal evolution of [$E_{\rm peak}$]{} is that of a $-1$ power law throughout. Since the picture becomes more complicated when physical processes are used to model the 