We systematically compute the annihilation rate for winos and higgsinos into the final state gamma + X. The radiative corrections to this process receive enhancement from the large Bloch-Nordsieck-Violating Sudakov logarithm, log(2 M_\chi/M_W). We resum the double logs and include single logs to fixed order using a formalism that combines nonrelativistic and soft-collinear effective field theories. For the wino case, we adapt an exclusion curve using results of the HESS experiment. At the thermal relic mass of 3 TeV, LL' corrections result in a ~30% reduction in rate relative to LL. Nonetheless, single logs do not save the wino, and it is still excluded by an order of magnitude. Experimental cuts produce an endpoint region which, our results show, significantly effects the higgsino rate at its thermal relic mass near 1 TeV and is deserving of further study.