Two new oxides, BaTeMo2O9 and BaTeW2O9, have been synthesized, by standard solid-state techniques, that have strong SHG intensities of approximately 600 x SiO2, on the order of LiNbO3. Both materials contain cations susceptible to second-order Jahn-Teller (SOJT) distortions, resulting in asymmetric coordination environments. The SOJT distortion polarizes the M6+-O and Te4+-O bonds. Equally importantly, these polarizations constructively add, resulting in the large SHG responses. Powder SHG measurements on BaTeM2O9 (M = Mo6+ or W6+) indicated that both materials are phase-matchable and have a deffexp of 28 and 22 pm/V, respectively. Using bond hyperpolarizability values (beta's) of 130 x 10-40 and 305 x 10-40 m4/V for Te4+-O and Mo6+-O respectively, we calculate a deffcalc of 20pm/V for BaTeMo2O9. In addition, through the powder SHG measurements, we are able to give a more reasonable value for beta(W6+-O), 230 x 10-40 m4/V. This value is consistent with the smaller polarizability and magnitude of the intra-octahedral distortion of W6+ compared with Mo6+.