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.