Human observers can detect their heading direction on a short time scale on the basis of optic flow. We investigated the visual perception and reconstruction of visually travelled two-dimensional (2-D) trajectories from optic flow, with and without a landmark. As in our previous study, seated, stationary subjects wore a head-mounted display in which optic-flow stimuli were shown that simulated various manoeuvres: linear or curvilinear 2-D trajectories over a horizontal plane, with observer orientation either fixed in space, fixed relative to the path, or changing relative to both. Afterwards, they reproduced the perceived manoeuvre with a model vehicle, whose position and orientation were recorded. Previous results had suggested that our stimuli can induce illusory percepts when translation and yaw are unyoked. We tested that hypothesis and investigated how perception of the travelled trajectory depends on the amount of yaw and the average path-relative orientation. Using a structured visual environment instead of only dots, or making available additional extra-retinal information, can improve perception of ambiguous optic-flow stimuli. We investigated the amount of necessary structuring, specifically the effect of additional visual and/or extra-retinal information provided by a single landmark in conditions where illusory percepts occur. While yaw was perceived correctly, the travelled path was less accurately perceived, but still adequately when the simulated orientation was fixed in space or relative to the trajectory. When the amount of yaw was not equal to the rotation of the path, or in the opposite direction, subjects still perceived orientation as fixed relative to the trajectory. This caused trajectory misperception because yaw was wrongly attributed to a rotation of the path: path perception is governed by the amount of yaw in the manoeuvre. Trajectory misperception also occurs when orientation is fixed relative to a curvilinear path, but not tangential to it. A single landmark could improve perception. Our results confirm and extend previous findings that, for unambiguous perception of ego-motion from optic flow, additional information is required in many cases, which can take the form of fairly minimal, visual information.