The tortuosity of retinal blood vessels is a diagnostic parameter assessed by ophthalmologists on the basis of examples and experience; no quantitative model is specified in clinical practice. All quantitative measures proposed to date for automatic image analysis purposes are functions of the curvature of the vessel skeleton. We suggest in this paper that curvature may not be the only quantity involved in modeling tortuosity, and that vessel thickness, or caliber, may also play a role. To support this statement, we devise a novel measure of tortuosity, depending on both curvature and thickness, and test it with 200 vessels selected by our clinical author from the public digital retinal images for vessel extraction database. Results are in good accordance with clinical judgment. Comparative experiments show performance similar to or better than that of four measures reported in the literature. We conclude that there is reasonable evidence supporting the investigation of tortuosity models incorporating more measurements than just skeleton curvature, and specifically vessel caliber.