Although new technology is widely used for detailed design and image manipulation, its use in the early stages of visual invention is much less common, one reason being that the denotation systems used in paper-and-pencil sketching assist creativity in ways that are poorly understood. Leonardo da Vinci advocated the use of untidy indeterminacies for working out composition, because he believed that they stimulated visual invention. Recent research in cognitive psychology suggests a mental-imagery model that expands Leonardo’s theory and provides evidence for cognitive mechanisms that clarify the function of familiar sketch attributes. Sketches may mediate mental translation between spatially depictive and structurally descriptive modes of visual representation. Evidence for a hybrid percept-image theory of ordinary paper sketching is briefly outlined. Some implications of this theory for the development of improved computer sketching systems are briefly discussed.