In inertial confinement fusion (ICF) experiments, irradiation uniformity is improved by passing laser beams through distributed phase plates (DPPs), which produce focused intensity profiles with well-controlled, reproducible envelopes modulated by fine random speckle. [C. B. Burckhardt, Appl. Opt.9, 695 (1970); Y. Kato and K. Mima, Appl. Phys. B29, 186 (1982); Y. Kato &etal;, Phys. Rev. Lett.53, 1057 (1984); Laboratory for Laser Energetics LLE Review 33, NTIS Document No. DOE/DP/40200-65, 1987 (unpublished), p. 1; Laboratory for Laser Energetics LLE Review 63, NTIS Document No. DOE/SF/19460-91, 1995 (unpublished), p. 1.] A uniformly ablating plasma atmosphere acts to reduce the contribution of the speckle to the time-averaged irradiation nonuniformity by causing the intensity distribution to move relative to the absorption layer of the plasma. This occurs most directly as the absorption layer in the plasma moves with the ablation-driven flow, but it is shown that the effect of the accumulating ablated plasma on the phase of the laser light also makes a quantitatively significant contribution. Analytical results are obtained using the paraxial approximation applied to the beam propagation, and a simple statistical model is assumed for the properties of DPPs. The reduction in the time-averaged spatial spectrum of the speckle due to these effects is shown to be quantitatively significant within time intervals characteristic of atmospheric hydrodynamics under typical ICF irradiation intensities. ©1997 American Institute of Physics.