We have developed computational techniques that allow image averaging to be applied to electron micrographs of filamentous molecules that exhibit tight and variable curvature. These techniques, which involve straightening by cubic-spline interpolation, image classification, and statistical analysis of the molecules' curvature properties, have been applied to purified brain clathrin. This trimeric filamentous protein polymerizes, both in vivo and in vitro, into a wide range of polyhedral structures. Contrasted by low-angle rotary shadowing, dissociated clathrin molecules appear as distinctive three-legged structures, called "triskelions" (E. Ungewickell and D. Branton (1981) Nature 289, 420). We find triskelion legs to vary from 35 to 62 nm in total length, according to an approximately bell-shaped distribution (μ = 51.6 nm). Peaks in averaged curvature profiles mark hinges or sites of enhanced flexibility. Such profiles, calculated for each length class, show that triskelion legs are flexible over their entire lengths. However, three curvature peaks are observed in every case: their locations define a proximal segment of systematically increasing length (14.0-19.0 nm), a mid-segment of fixed length (∼12 nm), and a rather variable end-segment (11.6-19.5 nm), terminating in a hinge just before the globular terminal domain (∼7.3 nm diameter). Thus, two major factors contribute to the overall variability in leg length: (1) stretching of the proximal segment and (2) stretching of the end-segment and/or scrolling of the terminal domain. The observed elasticity of the proximal segment may reflect phosphorylation of the clathrin light chains.