Density-functional calculations are used to study the electronic structure and transport properties of the type-I clathrates, K8Sn46, and K(8)Sn(44)square(2), (square is a missing Sn atom), and the type-III clathrate K8Sn25. We show K(8)Sn(44)square(2) to be more stable than the defect-free K8Sn46, with K8Sn46 being metallic and K(8)Sn(44)square(2); semimetallic. K8Sn25 is a zintl-phase semiconductor with a band gap of 0.5 eV. It has flatter bands than the type-I clathrates and can be expected to exhibit a smaller electrical conductivity but much larger Seebeck coefficient than the almost zintl K(8)Sn(44)square(2). The figure of merit of the type-III clathrate is an order of magnitude larger than its type-I counterparts. This would make a suitably doped K8Sn25 at least as good a thermoelectric as the best Ge-based type-I clathrates, and potentially better, depending on the momentum relaxation time for carriers in this material.