  By means of singularisations and insertions in Nakada's alpha-expansions,
which involves the removal of partial quotients 1 while introducing partial
quotients with a minus sign, the natural extension of Nakada's continued
fraction map T_alpha is given for (\sqrt{10}-2)/3\leq\alpha<1. From our
construction it follows that \Omega_\alpha, the domain of the natural extension
of T_\alpha, is metrically isomorphic to \Omega_g for \alpha \in [g^2,g), where
g is the small golden mean. Finally, although \Omega_\alpha proves to be very
intricate and unmanageable for \alpha \in [g^2, (\sqrt{10}-2)/3), the
\alpha-Legendre constant L(\alpha) on this interval is explicitly given.
