We have studied the competitive entry of potassium and sodium into carbon nanotubes using molecular dynamics simulations. Our results demonstrate how a combination of strong sodium hydration coupled with strong potassium-chlorine interaction leads to enhanced potassium selectivity at certain diameters. We detail the reasons behind this, and show how variation of nanotube diameter can cause a switch to sodium selectivity, or even cause a decrease in overall ion entry despite an increase in diameter. These results demonstrate the importance of considering inter-ion dependence in the theoretical study of pore selectivity and show that, with careful design, the practical separation of sodium and potassium is possible using diameter variation alone.