The suggestion of Krueger (1973) and other that wholistic processes underlie certain perceptual judgments is taken up in this paper. It is argued that properties such as bilateral symmetry can have a "diagnostic" significance for visual matching tasks. Diagnosticity means that if the property is present the appropriate response to a stimulus could theoretically be determined without any other analysis of the stimulus. Experiments 1 and 2 indicate that symmetry is exploited as a diagnostic property for the simultaneous same-different judgment. Displays that show the diagnostic form produce short reaction times. These experiments also show that the diagnosticity effect can be demonstrated independent of potentially confounding factors such as simplicity or redundancy. Experiments 3, 4, and 5 discount further confounding factors and also show that other properties, notably parallelism and colinearity of stimulus elements, can also be exploited as diagnostic in the simultaneous matching task. Diagnostics can have a structural or relational form. Diagnostic features are viewed as two-place structural predicates. Whether these diagnostics always have the same underlying form or not, the need for some representation of structure is a prerequisite for understanding even these simple recognition phenomena.