  The cold dark matter (DM) paradigm describes the large-scale structure of the
universe remarkably well. However, there exists some tension with the observed
abundances and internal density structures of both field dwarf galaxies and
galactic satellites. Here, we demonstrate that a simple class of DM models may
offer a viable solution to all of these problems simultaneously. Their key
phenomenological properties are velocity-dependent self-interactions mediated
by a light vector messenger and thermal production with much later kinetic
decoupling than in the standard case.
