Treisman and others have reported that the visual search for a target distinguished along a single stimulus dimension (for example, colour or shape) is conducted in parallel, whereas the search for an item defined by the conjunction of two stimulus dimensions is conducted serially. For a single dimension the target 'pops out' and the search time is independent of the number of irrelevant items in the set. For conjunctions, the search time increases as the set becomes larger. Thus, it seems that the visual system is incapable of conducting a parallel search over two stimulus dimensions simultaneously. Here we extend this conclusion for the conjunction of motion and colour, showing that it requires a serial search. We also report two exceptions: if one of the dimensions in a conjunctive search is stereoscopic disparity, a second dimension of either colour or motion can be searched in parallel.