  We use properties of doubly-magic nuclei and ab-initio calculations of
low-density neutron matter to constrain Skyrme equations of state for
neutron-rich conditions. All of these properties are consistent with a Skyrme
functional form and a neutron-matter equation of state that depends on three
parameters. With a reasonable range for the neutron-matter effective mass, the
values of the two other Skyrme parameters are well constrained. This leads to
predictions for other quantities. The neutron skins for $^{208}$Pb and
$^{48}$Ca are predicted to be 0.182(10) fm and 0.173(5) fm, respectively. Other
results including the dipole polarizability are discussed.
