We provide a new way of constraining the relative scintillation efficiency L_eff for liquid xenon. Using a simple estimate for the electronic and nuclear stopping powers together with an analysis of recombination processes we predict both the ionization and the scintillation yields. Using presently available data for the ionization yield, we can use the correlation between these two quantities to constrain L_eff from below. Moreover, we argue that more reliable data on the ionization yield would allow to verify our assumptions on the atomic cross sections and to predict the value of L_eff. We conclude that the relative scintillation efficiency should not decrease at low nuclear recoil energies, which has important consequences for the robustness of exclusion limits for low WIMP masses in liquid xenon Dark Matter searches. ; Comment: 11 pages, 6 figures. Version accepted in Astroparticle Physics. Enhanced discussion and additional figures