Nuclei in the $Zapprox100$ 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 $Zapprox100$ 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.
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