  Any form of dark matter which was in thermal equilibrium with the Standard
Model in the early Universe must have some annihilation mechanism in order to
avoid overclosure. In general, such models are now constrained by the negative
experimental results from colliders, direct detection, and indirect detection,
all of which are capable of probing interactions at the approximate strength
suggested by a thermal cross section. It is timely to consider what scenarios
of thermal dark matter which are still viable. In this paper we consider a
class of dark matter models which is designed to avoid many of the current
constraints: Majorana dark matter coupling to the Standard Model through
leptophilic singlet scalars and pseudoscalars. We show that requiring realistic
electroweak symmetry breaking generically forces the mediators to couple with
quarks, allowing these models to be constrained by the current experimental
data. We find that -- barring fine-tuning -- this type of thermal dark matter
is excluded by a combination of direct and indirect detection for masses below
$\sim 100$ GeV. Heavier dark matter is still viable, but in principle visible
via its indirect detection signature.
