  Maximizing nonlinear light-matter interactions is a primary motive for
compressing laser pulses to achieve ultrashort transform limited pulses. Here
we show how, by appropriately shaping the pulses, resonant multiphoton
transitions can be enhanced significantly beyond the level achieved by
maximizing the pulse's peak intensity. We demonstrate the counterintuitive
nature of this effect with an experiment in a resonant two-photon absorption,
in which, by selectively removing certain spectral bands, the peak intensity of
the pulse is reduced by a factor of 40, yet the absorption rate is doubled.
Furthermore, by suitably designing the spectral phase of the pulse, we increase
the absorption rate by a factor of 7.
