People are especially efficient in processing certain visual stimuli such as human faces or good configurations. It has been suggested that topology and geometry play important roles in configural perception. Visual search is one area in which configurality seems to matter. When either of 2 target features leads to a correct response and the sequence includes trials in which either or both targets are present, the result is a redundant-target paradigm. It is common for such experiments to find faster performance with the double target than with either alone, something that is difficult to explain with ordinary serial models. This redundant-targets study uses figures that can be dissimilar in their topology and geometry and manipulates the stimulus set and the stimulus-response assignments. The authors found that the combination of higher order similarity (e.g., topological) among the features in the stimulus set and response assignment can effectively overpower or facilitate the redundant-target effect, depending on the exact nature of the former characteristics. Several reasonable models of redundant-targets performance are falsified. Parallel models with the potential for channel interactions are supported by the data.