For second harmonic generation, when restricted to one space dimension and pure amplitude modulation, we establish a direct relation between the incident pulse-shape of the fundamental wave and the asymptotic pulse-shape of the harmonic wave. In particular, we show that the inverse problem - i.e., to determine the input pulse-shape in order to achieve a required output pulse-shape - is much easier to solve than the forward problem. (C) 2000 Elsevier Science B.V. All rights reserved.