I present recent work on improving constraints for fundamental constants from Big Bang Nucleosynthesis (BBN). After giving an idea of the general usefulness of using BBN as a laboratory to test theories beyond the standard model, the effects of varying the fine-structure constant and the Higgs vacuum expectation value (VEV) on primordial abundances are laid out. Using five publicly available codes, BBN is simulated with different values for these two constants and possible constraints on the variations are derived from experimental data of primordial light element abundances.