  Photons produced in the annihilations of dark matter particles can be
detected by gamma-ray telescopes; this technique of indirect detection serves
as a cornerstone of the upcoming assault on the dark matter paradigm. The main
obstacle to the extraction of information about dark matter from the
annihilation photons is the presence of large and uncertain gamma-ray
backgrounds. We present a new technique for using gamma-ray data to constrain
the properties of dark matter that makes minimal assumptions about the dark
matter and the backgrounds. The technique relies on two properties of the
expected signal from annihilations of the smooth dark matter component in our
galaxy: 1) it is approximately rotationally symmetric around the axis
connecting us to the Galactic Center, and 2) variations from the mean signal
are uncorrelated from one pixel to the next. We apply this technique to recent
data from the Fermi telescope to generate constraints on the dark matter mass
and cross section for a variety of annihilation channels. We quantify the
uncertainty introduced into our constraints by uncertainties in the halo
profile and by the possibility that the halo is triaxial. The resultant
constraint, the flux F \leq 4.5\times10^-6 cm^-2 s^-1 sr^-1 for energies
between 1 and 100 GeV at an angle 15 degrees away from the Galactic Center,
translates into an upper limit on the velocity weighted annihilation cross
section of order 10^-25 cm^3 s^-1 depending on the annihilation mode.
