New calculations of the quasi-bound state in the K − pp system using Faddeev-type equations in AGS form with coupledKN N and πΣN channels were performed. A chiralKN potential together with phenomenological models ofKN interaction with one-and two-pole structure of the Λ(1405) resonance were used. All three potentials reproduce experimental data on low-energy K − p scattering and kaonic hydrogen with the same level of accuracy. New method of calculating the subthreshold resonance position and width in a three-body system was proposed and used together with the direct search of the resonance pole. We obtained binding energy of the K − pp quasi-bound state ∼ 32 MeV with the chirally motivated and 47 − 54 MeV with the phenomenologicalKN potentials. The width is about 50 MeV for the two-pole models of the interaction, while the onepole potential gives ∼ 65 MeV width. The question of using an energy dependent potential in fewbody calculations is discussed in detail. It is shown that "self-consistent" variational calculations using such a potential are unable to produce a reasonable approximation to the exact result.