Single crystals of La2-xMxCuO4, where M is Na or K, have been prepared by precipitation from molten NaOH at 320-degrees-C or from molten KOH at 450-degrees-C. The composition of several individual crystals as determined by wavelength-dispersive X-ray fluorescence analysis averaged to La1.88Na0.12CuO4 and La1.79K0.21CuO4. Iodometric titrations on polycrystalline samples with identical compositions showed that the formal oxidation states for the Cu atoms are +2.19 and +2.31, respectively. On the basis of the analysis of single-crystal X-ray diffraction data, it has been determined that the alkali metal doped lanthanum copper oxides crystallize in a new structure type that is distinct from the analogous phases containing alkaline earth metal ions. The space group is P4/nmm, and lattice parameters are a = 3.766(1) angstrom, c = 13.216(5) angstrom for the Na-doped material and a = 3.7708(7) angstrom, c = 13.321(2) angstrom for the K-doped material. In these phases, the alkali metal ions are ordered in the rock-salt blocks, and the Cu atoms are displaced out of the plane toward the alkali metal ions. Despite this distortion of the CuO2 planes, both phases exhibit superconductivity, near 26 and 6 K, respectively.