The seeming contradiction that K+ channels conduct K+ ions at maximal throughput rates while not permeating the slightly smaller Na+ ion has perplexed scientists for decades. Although numerous models have addressed selective permeation in K+ channels, the combination of conduction efficiency and ion selectivity has not yet been linked through a unified functional model. Here, we investigate the mechanism of ion selectivity through atomistic simulations totalling more than 400 microseconds in length, which include over 7000 permeation events. Together with free-energy calculations, our simulations show that both rapid permeation of K+ and ion selectivity are ultimately based on a single principle: the direct knock-on of completely desolvated ions in the channels' selectivity filter. Herein, the strong interactions between multiple 'naked' ions in the four filter binding sites give rise to a natural exclusion of any competing ions. Our results are in excellent agreement with experimental selectivity data, measured ion interaction energies, and recent twodimensional infrared spectra of filter ion configurations.