  We demonstrate that significant effects in the "superluminal propagation"of
light-pulses cannot be observed without involving systems whose gain explodes
outside the pulse spectrum. We explicitly determine the minimum norm of the
gain to attain given superluminal effects and the transfer function of the
corresponding optimal system. The gain-norms which would be required with the
most efficient systems considered up to now (dispersive media, photonic
barriers) to attain the same effects are shown to exceed the minimum by several
orders of magnitude. We finally estimate the largest superluminal advances
which could be attained in a realistic experiment.
