  Dark matter (DM) coupled to light mediators has been invoked to resolve the
putative discrepancies between collisionless cold DM and galactic structure
observations. However, $\gamma$-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, $\gamma$-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.
