The possibility of driving the dense winds of Wolf-Rayet stars via multiple scattering of photons in resonance lines is examined. For the case of many overlapping lines it is found that the diffuse radiation arising from the multiple scattering process leads to a radiative acceleration grad even larger than the commonly used unattenuated flux models where each line is assumed to interact separately with the unattenuated photospheric flux. The radial dependence of grad in the outer parts of the wind is now weaker than r−2, which in turn leads to a steeper rise in the velocity field.