Higher-efficiency, lower-cost refrigeration is needed for both large- and small-scale cooling. Refrigerators using entropy changes during cycles of stretching or hydrostatic compression of a solid are possible alternatives to the vapor-compression fridges found in homes. We show that high cooling results from twist changes for twisted, coiled, or supercoiled fibers, including those of natural rubber, nickel titanium, and polyethylene fishing line. Using opposite chiralities of twist and coiling produces supercoiled natural rubber fibers and coiled fishing line fibers that cool when stretched. A demonstrated twist-based device for cooling flowing water provides high cooling energy and device efficiency. Mechanical calculations describe the axial and spring-index dependencies of twist-enhanced cooling and its origin in a phase transformation for polyethylene fibers.