The influence of quantum confinement on the one- and two-photon absorption spectra (1PA and 2PA) of PbS and PbSe semiconductor quantum dots (QDs) is investigated. The results show 2PA peaks at energies where only 1PA transitions are predicted and 1PA peaks where only 2PA transitions are predicted by the often used isotropic k x p four-band envelope function formalism. The first experimentally identified two-photon absorption peak coincides with the energy of the first one photon allowed transition. This first two-photon peak cannot be explained by band anisotropy, verifying that the inversion symmetry of the wave functions is broken and relaxation of the parity selection rules has to be taken into account to explain optical transitions in lead-salt QDs. Thus, while the band anisotropy of the bulk semiconductor plays a role in the absorption spectra, especially for the more anisotropic PbSe QDs, a complete model of the absorption spectra, for both 1PA and 2PA, must also include symmetry breaking of the quantum confined wave functions. These studies clarify the controversy of the origin of spectral features in lead-salt QDs.