  We investigate the possibility of fitting the putative spectrum of gamma-rays
from annihilating dark matter at the Galactic Center by a super-exponential
template. By generating and analyzing mock data for several ongoing and future
experiments (HESS, CTA and DMA), we find that the preference for a
super-exponential template (over an exponential) is especially strong for dark
matter annihilating to $\tau^+\tau^-$ and $\mu^+\mu^-$ relative to other
annihilation channels.
