In traditional electric machines, it is usually possible to achieve constant power high-speed operation by employing field weakening through the injection of a negative d-axis current component. However, in machines with low armature inductance, such as high power density permanent magnet synchronous machines, and more specifically, coreless machines, which are gaining increasing attention because of their high specific torque, the extended speed range obtained using this method is very narrow. This paper summarizes the performance characteristics of existing approaches for obtaining constant power operation and proposes two new techniques, specially applicable to coreless axial flux permanent magnet machine namely, current weakening and relative winding rotation.