This paper presents a design approach for interior permanent-magnet (IPM) machines with variable-flux characteristics using low-coercive-force magnets for improved efficiency and extended operating speed range. A flux-intensifying IPM type with L-d >L-q is used in the design due to positive I-d operation and reduced loaded I-q effects. Design considerations of machine structures and variable-flux machine attributes are discussed. In addition, leakage flux in a rotor is particularly designed to also obtain another flux-varying capability. Evaluation of the designed machine is provided by finite-element analysis simulations and experiments on a proof-of-principle machine. The designed machine shows benefits in increasing efficiency and speed range in a low-torque region when variable magnetization control of the low-coercive-force magnets or the design of the leakage flux proposed in this paper is implemented.