A theory is presented describing the electron cyclotron interaction at frequencies near cutoff, followed by a Cˇerenkov interaction region. In such a case, the cyclotron interaction withdraws only the orbital component of electron momentum, while in the Cˇerenkov interaction the electrons lose their axial momentum. It is shown that the addition of the Cˇerenkov interaction significantly enhances the total electronic efficiency. Since both kinds of operation are relatively insensitive to electron velocity spread, the efficiency of the combined interaction is also rather tolerant to velocity spread. Thus, rather efficient sources of electromagnetic radiation based on poor quality electron beams may be developed.