We calculate the linear growth rate of small-scale radiative instabilities for Wolf- Rayet (W-R) wind models driven by multiline scattering. Our approach involves a second-order extension of our previously developed nonisotropic-diffusion treatment of the multiline transfer. We confirm that the isotropizing effect of multiple scattering in such dense winds acts to suppress the instability, in comparison to the optically thin winds of OB stars. However, we also show that the inherent sphericity of the wind expansion leads to a significant residual instability.More specifically, the instability growth rate in W-R winds is reduced relative to the OB case by the ratio of the photon mean free path to the radius, λ/r, which is characteristically of order the inverse wind- momentum number, P-1wind = L*/Mdotυ∞c ∼ 0.1. Even with this reduction, the instability is generally still strong enough for base wind perturbations to be amplified by a very large number of e-folds (typically at least 40) by the time they exit the multiple-scattering region. This can be expected to lead to extensive wind structure, including strong clumping, throughout the observable part of the wind. Such extensively clumped wind structure could provide a natural explanation for the "moving bumps" commonly observed in optical emission-line spectra formed in W-R winds. It would also imply a reduction in mass-loss rates inferred from diagnostics sensitive to the square of the wind density.