  Light electroweakinos, the neutral and charged fermionic supersymmetric
partners of the Standard Model $\mathrm{SU}(2)\times\mathrm{U}(1)$ gauge bosons
and of the two $\mathrm{SU}(2)$ Higgs doublets, are an important target for
searches for new physics with the Large Hadron Collider (LHC). However, if the
lightest neutralino is the dark matter, constraints from direct dark matter
detection experiments rule out large swaths of the parameter space accessible
to the LHC, including in large part the so-called "well-tempered" neutralinos.
We focus on the Minimal Supersymmetric Standard Model (MSSM) and explore in
detail which regions of parameter space are not excluded by null results from
direct dark matter detection, assuming exclusive thermal production of
neutralinos in the early universe, and illustrate the complementarity with
current and future LHC searches for electroweak gauginos. We consider both
bino-Higgsino and bino-wino "not-so-well-tempered" neutralinos, i.e. we include
models where the lightest neutralino constitutes only part of the cosmological
dark matter, with the consequent suppression of the constraints from direct and
indirect dark matter searches.
