Organic-inorganic lead halide perovskites are a promising family of light absorbers for a new generation of solar cells, with reported efficiencies currently exceeding 22%. A common problem of solar cells fabricated using these materials is that their efficiency depends on their cycling history, an effect known as current-voltage (J-V) hysteresis. Potassium doping has recently emerged as a universal way to overcome this adverse phenomenon. While the atomistic origins of J-V hysteresis are still not fully understood, it is essential to rationalize the atomic-level effect of protocols that lead to its suppression. Here, using K-39 MAS NMR at 21.1 T we provide for the first time atomic-level characterization of the potassium-containing phases that are formed upon KI doping of multication and multianion lead halide perovskites. We find no evidence of potassium incorporation into 3D perovskite lattices of the recently reported materials. Instead, we observe formation of a mixture of potassium-rich phases and unreacted KI. In the case of Br-containing lead halide perovskites doped with KI, a mixture of KI and KBr ensues, leading to a change in the Br/I ratio in the perovskite phase with respect to the undoped perovskite. Simultaneous Cs and K doping leads to the formation of nonperovskite Cs/K lead iodide phases.