We present a general, model-independent formalism for determining bounds on the production of photons in dwarf spheroidal galaxies via dark matter annihilation, applicable to any set of assumptions about dark matter particle physics or astrophysics. As an illustration, we analyze gamma-ray data from the Fermi Large Area Telescope to constrain a variety of nonstandard dark matter models, several of which have not previously been studied in the context of dwarf galaxy searches.
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