Though guest-filled carbon nanotube yarns offer record performance as torsional and tensile artificial muscles, they are expensive, and only part of this muscle effectively contributes to actuation. We describe a muscle type that provides higher performance, in which the guest which drives actuation is a sheath on a twisted or coiled core that may be an inexpensive yarn. This shift from guest-filled to sheath-run artificial muscles increases the maximum work capacity by variables of 1.70 into 2.15 for tensile muscles driven electrothermally or from vapor absorption. A sheath-run electrochemical muscle creates 1.98 watts per g of average contractile electricity –40 times which for human muscle and 9.0 times that of the highest power alternative electrochemical muscle. Theory predicts the performance benefits of muscles that are sheath-run.