Abstract We address the problem of extracting single-nucleon momentum distributions n( p) from inclusive lepton scattering data. A model for these relates nuclear and nucleon structure functions (SF) through an intermediate SF f PN of a nucleus of point-particles. In addition to the asymptotic limit (AL), f PN contains, generally q-dependent, Final State Interactions (FSI) parts. In the inverse problem we employ the structure of the theory, but no numerical results, in order to separate q-dependent FSI from the AL, which depends on n( p). It appears that in the q-range of the analyzed lepton data, the FSI are only weakly q-dependent, making it virtually impossible to obtain parameters in a free fit of the parametrized components of f. Imposing we obtain n( p) for Fe and 4 He.