For ‘non-resonant’ reactions, a physical interpretation of the astrophysical factor S(E) in terms of the Coulomb barrier penetration factor and an intrinsic nuclear factor is proposed. Using the WKB (Wentzel, Kramers, Brillouin) approximation to evaluate the penetrabilities at stellar energies, we point out a drastic difference between the absolute values of S(0) according to whether s or p waves dominate the reaction. The variation with energy of S(E) to first order can also sign the nature of the wave. An application for the 6Li(d, α)4He and 7Li(p, α)4He reactions is presented. (Elsevier)