  Nuclei in the $Z\approx100$ mass region represent the heaviest systems where
detailed spectroscopic information is experimentally available. Although
microscopic-macroscopic and self-consistent models have achieved great success
in describing the data in this mass region, a fully satisfying precise
theoretical description is still missing.
  By using fine-tuned parametrizations of the energy density functionals, the
present work aims at an improved description of the single-particle properties
and rotational bands in the nobelium region. Such locally optimized
parameterizations may have better properties when extrapolating towards the
superheavy region.
  Skyrme-Hartree-Fock-Bogolyubov and Lipkin-Nogami methods were used to
calculate the quasiparticle energies and rotational bands of nuclei in the
nobelium region. Starting from the most recent Skyrme parametrization, UNEDF1,
the spin-orbit coupling constants and pairing strengths have been tuned, so as
to achieve a better agreement with the excitation spectra and odd-even mass
differences in $^{251}$Cf and $^{249}$Bk.
  The quasiparticle properties of $^{251}$Cf and $^{249}$Bk were very well
reproduced. At the same time, crucial deformed neutron and proton shell gaps
open up at $N=152$ and $Z=100$, respectively. Rotational bands in Fm, No, and
Rf isotopes, where experimental data are available, were also fairly well
described. To help future improvements towards a more precise description,
small deficiencies of the approach were carefully identified.
  In the $Z\approx100$ mass region, larger spin-orbit strengths than those from
global adjustments lead to improved agreement with data. Puzzling effects of
particle-number restoration on the calculated moment of inertia, at odds with
the experimental behaviour, require further scrutiny.
