The structures of 3+ states in Os have been debated over several decades. Based on measured B(E2) values they were interpreted in 186–192Os as Kπ = 4+ two-phonon vibrations, whereas inelastic scattering, and (t,α) work imply a hexadecapole phonon description. To clarify the nature of these Kπ = 4+ bands in 186,188Os, we performed a (3He,d) reaction on 185,187Re targets using 30 MeV 3He beams and a Q3D spectrograph. Absolute cross sections were obtained for excited states up to 3 MeV at 9 angles from 5° to 50°. Results indicate a significant 52+[402]π+32+[402]π component in agreement with quasiparticle phonon model predictions for a single hexadecapole phonon structure. [ABSTRACT FROM AUTHOR]