Non-yrast, excited states in neutron-rich 186 W were populated via inelastic-scattering reactions using beams of 136 Xe nuclei accelerated to 725 and 800 MeV. Levels populated in the reactions were investigated via particle-γ coincidence techniques using the Gammasphere array of High-Purity Germanium detectors and the compact heavy-ion counter, CHICO2. The K π = 2 + (γ), K π = 0 + and K π = 2 − (octupole) rotational side bands were extended to spins 14 , 12 , and 13 , respectively. A staggering pattern observed in the energies of levels in the K π = 2 + band was found to be consistent with a potential that gets softer to vibration in the γ degree of freedom with increasing spin. The odd-even staggering of states in the K π = 2 − band was found to exhibit a phase opposite to that seen in the γ band; an effect most probably associated with Coriolis coupling to other, unobserved octupole vibrational bands in 186 W.