Resonant optical transitions in asymmetric quantum wells yield huge second order optical nonlinearities but also strong absorption. It is shown that, under these specific conditions where the conversion length may be far smaller than the coherence length, the second harmonic generation equations can be put into a simple dimensionless form. The influence of the quantum well parameters on the optical nonlinearities may thus be easily studied. It is shown that, by optimizing these parameters, second harmonic generation efficiency as large as 20% may be obtained for moderate pump power (≊15 MW/cm2, i.e., before saturation) without any phase match procedure.