The existence of super-heavy nuclei can only be explained by the introduction of stabilizing ground state shell effects. The macroscopic-microscopic masses are constructed from the sum of a macro-scopic, liquid-drop, energy contribution and a microscopic, shell-correction energy. In the present study, shell-correction energies are inferred by subtracting the liquid-drop contributions to their corresponding experimental masses. As most super-heavy nuclei masses are not precisely known, they are deduced from measured Qα values. Furthermore, a detailed uncertainty analysis regarding experimental masses and more importantly the liquid-drop masses delivers decisive theoretical constraints on shell-correction energies. The current work focuses on two α decay chains, the first, following from a hot fusion reaction leading to the synthesis of 291 Lv and the second, following from a cold fusion reaction leading to the synthesis of 277 Cn. Contrasting the outcomes obtained for these two decay chains, demonstrates that mass measurement precisions of about 50 keV are required in order to efficiently constrain the shell-correction energies of super-heavy nuclei.