The beam quality of diode-pumped alkali lasers (DPALs) is of major concern in the studies of these lasers. We report on experimental studies and modeling of the beam propagation factor M2 in flowing-gas Cs DPALs with stable optical resonators and of its dependence on the resonator geometry. The measured values of M2 are in agreement with those calculated using the optical model of multi-transverse mode operation (Auslender et al. in Opt Express 25:19767, 2017). Conditions for substantial improvement of the output laser beam quality, reducing M2 to close to unity, are found. Changing the length of the resonator, and/or the radius of curvature of the high reflection mirror, leaving all other parameters of the laser unchanged, makes it possible to control the beam quality. Techniques for controlling M2 in DPALs with wide-aperture beams have not been studied elsewhere and are very important for the applications of this laser. In addition to the optical model, a simple analytical method based on the model suggested by Siegman (IEEE J Quantum Electron 29:1212, 1993) is applied to the experimental results and predicts a simple scaling law for M2 as a function of the size of the resonator fundamental mode.