  The Minimal Supersymmetric Standard Model (MSSM) is under intense scrutiny at
the LHC and in dark matter searches. Interestingly, scenarios with light
squarks of the third generation remain not only viable, but also well motivated
by the observed Standard-Model-like Higgs boson mass and dark matter relic
density. The latter often requires important contributions from squark pair
annihilation. Following up on previous work, we present in this paper a
precision analysis of squark pair annihilation into quarks at next-to-leading
order of QCD including Sommerfeld enhancement effects. We discuss all technical
details of our one-loop, real emission and resummation calculations, their
implementation in the precision tool DM@NLO, as well as the numerical impact on
the annihilation cross section and cosmological relic density in
phenomenological MSSM scenarios respecting in particular current LHC
constraints. We demonstrate that including these radiative corrections leads to
substantial shifts in the preferred parameter regions by up to 20 GeV.
