  We consider dark matter models in which the mass splitting between the dark
matter particles and their annihilation products is tiny. Compared to the
previously proposed Forbidden Dark Matter scenario, the mass splittings we
consider are much smaller, and are allowed to be either positive or negative.
To emphasize this modification, we dub our scenario "Impeded Dark Matter". We
demonstrate that Impeded Dark Matter can be easily realized without requiring
tuning of model parameters. For negative mass splitting, we demonstrate that
the annihilation cross-section for Impeded Dark Matter depends linearly on the
dark matter velocity or may even be kinematically forbidden, making this
scenario almost insensitive to constraints from the cosmic microwave background
and from observations of dwarf galaxies. Accordingly, it may be possible for
Impeded Dark Matter to yield observable signals in clusters or the Galactic
center, with no corresponding signal in dwarfs. For positive mass splitting, we
show that the annihilation cross-section is suppressed by the small mass
splitting, which helps light dark matter to survive increasingly stringent
constraints from indirect searches. As specific realizations for Impeded Dark
Matter, we introduce a model of vector dark matter from a hidden $SU(2)$
sector, and a composite dark matter scenario based on a QCD-like dark sector.
