  We show that for a neutrino factory baseline of $L \sim 7300 km - 7 600 km$ a
``clean'' measurement of $\sin^2 2 \theta_{13}$ becomes possible, which is
almost unaffected by parameter degeneracies. We call this baseline "magic"
baseline, because its length only depends on the matter density profile. For a
complete analysis, we demonstrate that the combination of the magic baseline
with a baseline of 3000 km is the ideal solution to perform equally well for
the $\sin^2 2 \theta_{13}$, sign of $\Delta m_{31}^2$, and CP violation
sensitivities. Especially, this combination can very successfully resolve
parameter degeneracies even below $\sin^2 2 \theta_{13} < 10^{-4}$.
