The nonlinear optical properties of quantum wells (QWs) represented by a Poschl-Teller confining potential are studied. This potential is well suited for such purposes as it can easily become asymmetrical by a correct choice of its parameter set. We calculate the linear and the third-order nonlinear optical intersubband absorption coefficients, the second-harmonic generation (SHG) susceptibility tensor, and optical rectification (OR) under the density matrix formalism. Numerical results for a typical GaAs QW are presented. The resulting SHG and the OR coefficients are much larger than their values for bulk GaAs.