  Nuclear binding energies are investigated in two variants of the Skyrme
model: the first replaces the usual Skyrme term with a term that is sixth order
in derivatives, and the second includes a potential that is quartic in the pion
fields. Solitons in the first model are shown to deviate significantly from
ans\"atze previously assumed in the literature. The binding energies obtained
in both models are lower than those obtained from the standard Skyrme model,
and those obtained in the second model are close to the experimental values.
