Evaluated nuclear data for 186Re identify the majority of spin-parity assignments as tentative, with approximate values for the energies of several levels and transitions. In particular, the absence of known transitions that feed the J = 8+ isomer 186mRe motivates their discovery. This isomer, which has a half-life of 2 105 years, has a potential application in an isomer power source. Additionally, the isomer s role in certain nucleosynthesis processes is not well understood, so measured cross sections for transitions that feed the isomer would have astrophysical implications. Using the GErmanium Array for Neutron Induced Excitations (GEANIE) spectrometer at the Los Alamos Neutron Science Center (LANSCE), (n,2n ) and (n,n ) reactions in a 99.52% enriched 187Re target were used to obtain -ray spectra from 186Re and 187Re, respectively. The experimental data reveal 5 new transitions in186Re and 4 new transitions in 187Re. Similarities between the level schemes of 184Re and 186Re suggest that one of the newly-observed transitions in 186Re feeds the isomer from a level at 414.9 keV. The -ray energy measured for this transition implies an isomer energy of 148.2(5) keV, which is a significant improvement over the adopted value of 149(7) keV