The proton states in 187Re, 189Re, and 191Re have been studied using the (t,α) reaction. The beam of 15 MeV tritons was obtained from the Los Alamos Scientific Laboratory model FN tandem Van de Graaff accelerator. The reaction products were analyzed with a Q3D magnetic spectrometer and detected with a helical-cathode position sensitive proportional counter. Previous assignments for 187Re are adopted, and assignments in 189Re are based on characteristic intensity patterns and a previous γ-decay study. The Nilsson orbitais 5/2+, 9/2−, and 1/2+ are identified in 189Re, and possible assignments of these orbitals are suggested for 191Re. It is found that the spectroscopic strengths of low-lying 11/2− states are much smaller than would be expected for pure h11/2 shell model states but are consistent with values expected for a deformed model. However, the basic Nilsson model does not describe all the features well. The results are compared with the predictions of the Nilsson model with a hexadecapole deformation included.