The Octans association is one of several young stellar moving groups recently discovered in the Solar neighbourhood and hence a valuable laboratory for studies of stellar, circumstellar disc and planetary evolution. However, a lack of low-mass members or any members with trigonometric parallaxes means the age, distance and space motion of the group are poorly constrained. To better determine its membership and age, we present the first spectroscopic survey for new K- and M-type Octans members, resulting in the discovery of 29 UV-bright K5-M4 stars with kinematics, photometry and distances consistent with existing members. Nine new members possess strong LiI 6708 absorption, which allow us to estimate a lithium age of 30-40Myr, similar to that of the Tucana-Horologium association and bracketed by the firm lithium depletion boundary ages of the beta Pictoris (20Myr) and Argus/IC 2391 (50Myr) associations. Several stars also show hints in our medium-resolution spectra of fast rotation or spectroscopic binarity. More so than other nearby associations, Octans is much larger than its age and internal velocity dispersion imply. It may be the dispersing remnant of a sparse, extended structure which includes some younger members of the foreground Octans-Near association recently proposed by Zuckerman and collaborators.