  We present a systematic analysis of the description of odd nuclei by the
Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and
blocking of the odd nucleon. Current and spin densities in the Skyrme
functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on
basic properties (binding energies, odd-even staggering, separation energies
and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6,
and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z <
92 are considered. The calculations demonstrate that the TOMF effect is
generally small, although not fully negligible. The influence of the Skyrme
parameterization and the consistency of the calculations are much more
important. With a proper choice of the parameterization, a good description of
binding energies and their differences is obtained, comparable to that for even
nuclei. The description of low-energy excitation spectra of odd nuclei is of
varying quality depending on the nucleus.
