We describe how twist could play an essential role in stabilizing 20 nm diameter sickle hemoglobin fibers. Our theory successfully reproduces the observed variation of helical pitch length with fiber diameter. With no remaining adjustable parameters it also yields a prediction for the torsional rigidity of sickle hemoglobin fibers that is in good agreement with experiment and hence retains the striking feature that such fibers can be highly mechanically anisotropic, even with a ratio of bending to torsional rigidity of about 50. We discuss how our study might be relevant to the development of treatment strategies.