  We present first principle calculations of the structural and electronic
properties of the CuS covellite material. Symmetry-lowering structural
transition is well reproduced. However, the microscopic origin of the
transition is unclear. The calculations firmly establish that the so far
controversial Cu valency in this compound is 1.33. We also argue that recently
reported high-temperature superconductivity in CuS is unlikely to occur in the
stoichiometric defect-free material, since the determined Cu valency is too
close to 1 to ensure proximity to a Mott-Hubbard state and superexchange spin
fluctuations of considerable strength. On the other hand, one can imagine a
related system with more holes per Cu in the same structural motif ($e.g.$, due
to defects or O impurities) in which case combination of superexchange and an
enlarged compared to CuS Fermi surface may lead to unconventional
superconductivity, similar to HTSC cuprates, but, unlike them, of an $f$-wave
symmetry.
