The velocity spread existing on a velocity‐modulated electron beam of finite diameter is investigated as a function of drive, drift length, and perveance using a digital computer program based on a disk electron model. At small signal levels the velocity modulation decreases cosinusoidally to zero with drift distance in accordance with one‐dimensional bunching theory. At higher signal levels, however, the velocity spread does not go to zero due to aberrations introduced by the finite diameter of the beam.The minimum velocity spread at maximum bunching is found to be proportional to the square of the fundamental component of rf current, up to an optimum drive level. Above this drive level the velocity spread increases rapidly with no corresponding increase in rf current. Trajectories of electrons of all initial phases are found to undergo a basic transition from nonovertaking to overtaking at a new characteristic distance &lgr;pq/4, which is given approximately by the geometric mean of the infinite beam quarter‐plasma wavelength &lgr;p/4 and the reduced (due to finite beam size) quarter‐plasma wavelength &lgr;q/4. This characteristic distance is found to be a key parameter in the prediction of velocity spread, drift length and drive for optimally bunched electron beams for use in klystron amplifiers, harmonic generators, and in linear accelerators.