  We present a survey of the phenomenological adjustment of the parameters of
the Skyrme-Hartree-Fock (SHF) model for a self-consistent description of
nuclear structure and low-energy excitations. A large sample of reliable input
data from nuclear bulk properties (energy, radii, surface thickness) is
selected guided by the criterion that ground-state correlations should remain
small. Least squares fitting techniques are used to determine the SHF
parameters which accommodate best the given input data. The question of the
predictive value of the adjustment is scrutinized by performing systematic
variations with respect to chosen nuclear matter properties (incompressibility,
effective mass, symmetry energy, and sum-rule enhancement factor). We find that
the ground-state data, although representing a large sample, leave a broad
range of choices, i.e. a broad range of nuclear matter properties. Information
from giant resonances is added to pin down more precisely the open features. We
then apply the set of newly adjusted parameterizations to several more detailed
observables such as neutron skin, isotope shifts, and super-heavy elements. The
techniques of least-squares fitting provide safe estimates for the
uncertainties of such extrapolations. The systematic variation of forces allows
to disentangle the various influences on a given observable and to estimate the
predictive value of the SHF model. The results depend very much on the
observable under consideration.
