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The indirect detection of dark matter requires that dark matter annihilation products be discriminated from conventional astrophysical backgrounds. Here, we re-analyze GeV-band gamma-ray observations of the prominent Milky Way dwarf satellite galaxy Segue 1, for which the expected astrophysical background is minimal. We explicitly account for the angular extent of the conservatively expected gamma-ray signal and keep the uncertainty in the dark-matter profile external to the likelihood analysis of the gamma-ray data.