Structure from motion (SFM) is the ability to perceive three-dimensional structure from stimuli containing only two-dimensional motion signals and this ability seems to be a result of high-level cortical processes. It has long been thought that local motion signals defined by second-order cues only weakly contribute to perception of SFM since performance on purely second-order SFM tasks is poor, relative to first-order stimuli. We hypothesized that the mechanisms responsible for deriving SFM were insensitive to low-level stimulus attributes such as the first- or second-order nature of the dots composing the stimulus, in other words: that they were "cue-invariant", but that large differences in sensitivity to local first- and second-order motions were responsible for previous findings. By manipulating the relative strength of first-order dots in an SFM stimulus that combines first- and second-order dots, we show that the two types of motion can separately support SFM and co-operatively interact to produce vivid three-dimensional percepts. This provides strong support that the mechanisms underlying SFM are cue-invariant.