  The light mediator scenario of self-interacting dark matter is strongly
constrained in many ways. After summarizing the various constraints, we discuss
minimal options and models which allow to nevertheless satisfy all these
constraints. One straightforward possibility arises if the dark matter and
light mediator particles have a temperature sizably smaller than the SM
particles. Another simple possibility arises if dark matter doesn't annihilate
dominantly into a pair of light mediators but into heavier particles. Both
possibilities are discussed with scalar as well as vector boson light
mediators. Further possibilities, such as with a hierarchy of quartic scalar
couplings, are also identified.
