  The effects of Landau level mixing and finite thickness of the
two-dimensional electron gas on the relative stability of skyrmion and single
spin-flip excitations at Landau level filling factor $\nu=1$ have been
investigated. Landau level mixing is studied by fixed-phase diffusion Monte
Carlo and finite thickness is included by modifying the effective Coulomb
interaction. Both Landau level mixing and finite thickness lower skyrmion
excitation energies and favor skyrmions with fewer spin flips. However, the two
effects do not work `coherently'. When finite thickness is included the effect
of Landau level mixing is strongly suppressed.
