Excited states of lSSHg have been investigated via the 161Dy(ZSSi, 4n) reaction at 145 MeV. In-beam 7-ray spectroscopic studies have been performed with the "Chfiteau de Cristal" 4rc-multidetector array. A level scheme of t85Hg has been established. Shape coexistence, still present in lSSHg like in the neighbouring Hg isotopes, manifests itself through a weakly populated decoupled band built on the 13/2 § isomer and three stronglycoupled bands built on the prolate 1/2-[521], 7/2-1-514], and 9/2 + [624] Nilsson states.