We present a nonlinear analysis of the single‐particle dynamics in an electron cyclotron maser oscillator and show that the efficiency can be dramatically enhanced by appropriately contouring the system parameters. The beam electrons can be prebunched in phase to form a macroparticle in phase space such that beam kinetic energy is not extracted. After forming a phase‐bunched electron beam, either the applied magnetic field or the cavity electromagnetic field can be spatially varied in such a way as to extract virtually all the electron transverse kinetic energy. Without such contouring, the transverse efficiency is typically ?40%. An example is presented in which the transverse efficiency is increased from 36% (in uniform fields) to 75% by increasing the applied magnetic field by ∼6%. The present analysis can readily be extended to the case of a maser amplifier.