  Crystal structure, electronic state of Ir$^{4+}$, and magnetic properties of
the antifluorite compound K$_2$IrBr$_6$ are studied using high-resolution
synchrotron x-ray diffraction, resonant inelastic x-ray scattering (RIXS),
thermodynamic and transport measurements, and ab initio calculations. The
crystal symmetry is reduced from cubic at room temperature to tetragonal below
170 K and eventually to monoclinic below 122 K. These changes are tracked by
the evolution of the non-cubic crystal-field splitting $\Delta$ measured by
RIXS. Non-monotonic changes in $\Delta$ are ascribed to the competing effects
of the tilt, rotation, and deformation of the IrBr$_6$ octahedra as well as
tetragonal strain on the electronic levels of Ir$^{4+}$. The N\'eel temperature
of $T_N=11.9$ K exceeds that of the isostructural K$_2$IrCl$_6$, and the
magnitude of frustration on the fcc spin lattice decreases. We argue that the
replacement of Cl by Br weakens electronic correlations and enhances magnetic
couplings.
