Excited states in the odd-odd, highly neutron-deficient nucleus 166 Re have been investigated via the 92 Mo( 78 Kr, 3p1n) 166 Re reaction. Prompt γ rays were detected by the JUROGAM II γ -ray spectrometer, and the recoiling fusion-evaporation products were separated by the recoil ion transport unit (RITU) gas-filled recoil separator and implanted into the Gamma Recoil Electron Alpha Tagging spectrometer located at the RITU focal plane. The tagging and coincidence techniques were applied to identify the γ -ray transitions in 166 Re, revealing two collective, strongly coupled rotational structures, for the first time. The more strongly populated band structure is assigned to the πh 11/2 [514]9/2 − ⊗ νi 13/2 [660]1/2 + Nilsson configuration, while the weaker structure is assigned to be built on a two-quasiparticle state of mixed πh 11/2 [514]9/2 − ⊗ ν[h 9/2 f 7/2 ]3/2 − character. The configuration assignments are based on the electromagnetic characteristics and rotational properties, in comparison with predictions from total Routhian surface and particle-rotor model calculations.