Dark matter (DM) coupled to light mediators has been invoked to
resolve the putative discrepancies between collisionless cold DM and
galactic structure observations. However, \gammaγ-ray
searches and the CMB strongly constrain such scenarios. To ease the
tension, we consider asymmetric DM. We show that, contrary to the common
lore, detectable annihilations occur even for large asymmetries, and
derive bounds from the CMB, \gammaγ-ray,
neutrino and antiproton searches. We then identify the viable space for
self-interacting DM. Direct detection does not exclude this scenario,
but provides a way to test it.