Two new oxides have been unambiguously identified as Bi2Tc2O7-delta with delta = 0.14(1) and Bi3TcO8 through X-ray absorption near-edge structure spectroscopy and neutron powder diffraction. The compound Bi2Tc2O7-delta has a cubic pyrochlore-type structure with a = 10.4746(1) A, space group Fd3m (origin choice 2), and Z = 8. The compound Bi3TcO8 is also cubic, a = 11.5749(1) A, space group P2(1)3, Z = 8, and has a fluorite-related crystal structure. In Bi2Tc2O7-delta the Tc(IV) cations are octahedrally coordinated, whereas in Bi3TcO8 the Tc(VII) cations are tetrahedrally coordinated. A third new phase, probably Bi3Tc3O11, could not be obtained pure, but preliminary X-ray powder diffraction data affords a primitive cubic lattice with a = 9.3433(1) A. On the basis of structural similarities between Bi2Tc2O7-delta and closely related oxides, Bi2Tc2O7-delta is expected to be a metallic oxide with Pauli paramagnetism. Electronic structure calculations of both Bi2Tc2O7-delta and Bi3TcO8 further support metallic conductivity in the former and insulating behavior in the latter. The inert pair effect of the Bi cations on the crystal structures of Bi2Tc2O7-delta and Bi3TcO8 is also described. In addition, calculations of the valence electron localization function for Bi2Tc2O7-delta and Bi3TcO8 provide further visualization of the Bi 6s(2) lone pair electrons in the real space of the crystal structures.