Excited states in the neutron-deficient nuclei 163 75 Re88 and 165 75 Re90 were populated in the 106Cd(60Ni, p2nγ ) and 92Mo(78Kr, 3p2nγ ) fusion-evaporation reactions at bombarding energies of 270 and 380 MeV, respectively. γ rays were detected at the target position using the JUROGAM spectrometer while recoiling ions were separated in-flight by the RITU gas-filled recoil separator and implanted in the GREAT spectrometer. The energy level schemes for 163Re and 165Re were identified using recoil-decay correlation techniques. At low spin, the yrast bands of these isotopes consist of signature partner bands based on a single πh11/2 quasiproton configuration. The bands display large energy splitting consistent with the soft triaxial shape typical of transitional nuclei above N = 82. The configurations of the excited states are proposed within the framework of the cranked shell model.