Although guest-filled carbon nanotube yarns provide record performance as torsional and tensile artificial muscles, they are expensive, and only part of the muscle effectively contributes to actuation. We describe a muscle type that provides higher performance, in which the guest that drives actuation is a sheath on a twisted or coiled core that can be an inexpensive yarn. This change from guest-filled to sheath-run artificial muscles increases the maximum work capacity by factors of 1.70 to 2.15 for tensile muscles driven electrothermally or by vapor absorption. A sheath-run electrochemical muscle generates 1.98 watts per gram of average contractile power—40 times that for human muscle and 9.0 times that of the highest power alternative electrochemical muscle. Theory predicts the observed performance advantages of sheath-run muscles.