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.