Contrast thresholds for stereopsis were measured for a variety of bandpass-filtered random-dot stereograms in a series of experiments. The principal finding was that contrast thresholds for stereopsis from 'complex' stereograms composed of mixtures of (a) two widely different spatial frequencies or (b) two or more widely different oriented random textures, are considerably lower than would be expected if stereopsis from such stimuli is mediated by the first component to rise above its own stereopsis contrast threshold. Instead, it appears that stereopsis comes about whenever the supradetection-threshold contrast of a stereogram exceeds a certain level, regardless of whether this contrast is provided by a single component or by a mix of two different ones. The implications of these findings for models of stereopsis are discussed.