To fulfill the broadband tunability of the gyrotron backward-wave oscillator (gyro-BWO), stability issues are studied and displayed in the form of stability maps. These maps serve as a guide for the identification and optimization of stable windows for broadband tuning. A Ka-band gyro-BWO experiment was conducted accordingly. In the case of a short interaction length, stable and smooth tunability of 1.3 GHz was demonstrated with a peak interaction efficiency of 29.8%. In the longer length case, piecewise-stable tuning curves were obtained, as predicted in theory.