The effect of variations of the fundamental nuclear parameters on big-bang nucleosynthesis are modeled and discussed in detail taking into account the interrelations between the fundamental parameters arising in unified theories. Considering only 4He, strong constraints on the variation of the neutron lifetime, neutron-proton mass difference are set. We show that a variation of the deuterium binding energy is able to reconcile the 7Li abundance deduced from the WMAP analysis with its spectroscopically determined value while maintaining concordance with D and 4He.