Criteria are presented for J-band coaxial Gunn oscillators (where stray effects become very important) regarding the design and optimization of the microwave circuitry, the tuning element (varactor) and the active device (Gunn diode) in view of wideband tuning with high speeds but without a reduction of the circuit Q-factor in order to maintain a good noise performance. More than 2 GHz frequency shifts have been experimentally achieved at J-band by making use of the developed optimization criteria.