An insulated composite power cable having a wire core defining a common longitudinal axis, a multiplicity of composite wires around the wire core, and an insulative sheath surrounding the composite wires. In some embodiments, a first multiplicity of composite wires is helically stranded around the wire core in a first lay direction at a first lay angle defined relative to a center longitudinal axis over a first lay length, and a second multiplicity of composite wires is helically stranded around the first multiplicity of composite wires in the first lay direction at a second lay angle over a second lay length, the relative difference between the first lay angle and the second lay angle being no greater than about 4°. The insulated composite cables may be used for underground or underwater electrical power transmission. Methods of making and using the insulated composite cables are also described.