The effect of a random phase screen on laser beam wander in a turbulent atmosphere is studied theoretically. The photon distribution function method is used to describe the photon kinetics of both weak and strong turbulence. By bringing together analytical and numerical calculations, we have obtained the variance of beam centroid deflections caused by scattering on turbulent eddies. It is shown that an artificial distortion of the initial coherence of the radiation can be used to decrease the wandering effect. The physical mechanism responsible for this reduction and the applicability of our approach are discussed.