Two examples of how the SBPL (blue) and Band (red) function fit a synthetic synchrotron spectrum (green). Top: an example where the SBPL models the synchrotron (W = −1.4, θ = 128) emission adequately while the Band function is too narrow and artificially softens β to compensate. Bottom: both the SBPL and Band functions are poor approximations of the true synchrotron spectrum (W = −1.6, θ = 170) and hence would result in poor empirical inference about the true underlying mechanism.