  The precision measurement and discovery potential of a neutrino factory based
on a storage ring of boosted radioactive ions ($\beta$-beam) is re-examined. In
contrast with past designs, which assume ion $\gamma$ factors of $\sim 100$ and
baselines of L=130 km, we emphasize the advantages of boosting the ions to
higher $\gamma$ and increasing the baseline proportionally. In particular, we
consider a medium-$\gamma$ scenario ($\gamma \sim 500$, L=730 km) and a
high-$\gamma$ scenario ($\gamma \sim 2000$, L = 3000 km).The increase in
statistics, which grow linearly with the average beam energy, the ability to
exploit the energy dependence of the signal and the sizable matter effects at
this longer baseline all increase the discovery potential of such a machine
very significantly.
