Studies of the K-Ba-Ga-Sn system produced the clathrate compounds K(0.8(2))Ba(15.2(2))Ga(31.0(5))Sn(105.0(5)) [a = 17.0178 (4) Å], K(4.3(3))Ba(11.7(3))Ga(27.4(4))Sn(108.6(4)) [a = 17.0709 (6) Å] and K(12.9(2))Ba(3.1(2))Ga(19.5(4))Sn(116.5(4)) [a = 17.1946 (8) Å], with the type-II structure (cubic, space group Fd3m), and K(7.7(1))Ba(0.3(1))Ga(8.3(4))Sn(37.7(4)) [a = 11.9447 (4) Å], with the type-I structure (cubic, space group Pm3n). For the type-II structures, only the smaller (Ga,Sn)24 pentagonal dodecahedral cages are filled, while the (Ga,Sn)28 hexakaidecahedral cages remain empty. The unit-cell volume is directly correlated with the K:Ba ratio, since an increasing amount of monovalent K occupying the cages causes a decreasing substitution of the smaller Ga in the framework. All three formulae have an electron count that is in good agreement with the Zintl-Klemm rules. For the type-I compound, all framework sites are occupied by a mixture of Ga and Sn atoms, with Ga showing a preference for Wyckoff site 6c. The (Ga,Sn)20 pentagonal dodecahedral cages are occupied by statistically disordered K and Ba atoms, while the (Ga,Sn)24 tetrakaidecahedral cages encapsulate only K atoms. Large anisotropic displacement parameters for K in the latter cages suggest an off-centering of the guest atoms.