High-power, high-frequency gyrotrons for electron cyclotron resonance heating and current drive, such as proposed for the demonstration thermonuclear fusion reactor DEMO, require operating modes of very high order. As it is shown, the selection of the operating modes for such gyrotrons can be based on multi-frequency operability. A general selection strategy is derived, suitable for multi-purpose multi-frequency gyrotrons with quasi-optical mode converter and single-disc output window. Two examples, one of them relevant for future DEMO gyrotron designs, are discussed.