  The rational map ansatz of Houghton et al \cite{HMS} is generalised by
allowing the profile function, usually a function of $r$, to depend also on $z$
and $\bar{z}$. It is shown that, within this ansatz, the energies of the lowest
$B=2,3,4$ field configurations of the SU(2) Skyrme model are closer to the
corresponding values of the true solutions of the model than those obtained
within the original rational map ansatz. In particular, we present plots of the
profile functions which do exhibit their dependence on $ z$ and $\bar{z}$.
  The obvious generalisation of the ansatz to higher SU(N) models involving the
introduction of more projectors is briefly mentioned.
