We illustrate that the baseline Neutrino Factory configuration being developed within the International Design Study for the Neutrino Factory (the IDS-NF) is optimized for standard oscillation-physics measurements and for searches for new physics. For small values of θ13 (sin2 2θ13 < 10−2 ) a Neutrino Factory with two storage rings in which 25 GeV muons decay, pointing to two neutrino detectors, one situated at a distance between 2500 to 5000 km, the second between 7000 and 8000 km is optimal. If the value of θ13 is found to be large (sin2 2θ13 > 10−2 ), a Neutrino Factory in which 10 GeV muons are stored in a single ring provides the best sensitivity for the discovery of CP violation in the neutrino sector, the determination of the neutrino mass hierarchy and the measurement of θ13.