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This paper proposes a new experimental framework within which evidence regarding the perceptual characteristics of a visualization method can be collected, and describes how this evidence can be explored to discover principles and insights to guide the design of perceptually near-optimal visualizations. We make the case that each of the current approaches for evaluating visualizations is limited in what it can tell us about optimal tuning and visual design. We go on to argue that our new approach is better suited to optimizing the kinds of complex visual displays that are commonly created in visualization. Our method uses human-in-the-loop experiments to selectively search through the parameter space of a visualization method, generating large databases of rated visualization solutions. Data mining is then used to extract results from the database, ranging from highly specific exemplar visualizations for a particular data set, to more broadly applicable guidelines for visualization design. We illustrate our approach using a recent study of optimal texturing for layered surfaces viewed in stereo and in motion. We show that a genetic algorithm is a valuable way of guiding the human-in-the-loop search through visualization parameter space. We also demonstrate several useful data mining methods including clustering, principal component analysis, neural networks, and statistical comparisons of functions of parameters.