The equation of state and electronic structure of body-centered cubic potassium are investigated theoretically by the quantum-mechanical SAPW method. The results predict a series of pressure-induced electronic phase changes brought about by the sequential filling of initially unoccupied d-like electronic states. In addition to the discontinuous density changes that accompany these phase transitions, the presence of the d-like bands makes potassium extremely compressible. At pressures as low as 500 kb (0¿K), the ionic radius of potassium becomes compatible with that of iron and its electronic structure becomes like that of a typical transition metal. These properties should greatly enhance the miscibility of potassium in iron or iron-sulfide melts.