Using the results of direct, numerically exact computer solutions of the Maxwell equations, we analyze scattering and absorption characteristics of polydisperse compound particles in the form of wavelength-sized spheres covered with a large number of much smaller spherical grains. The results pertain to the complex refractive indices 1.55 + i0.0003, 1.55 +i0.3, and 3 + i0.1. We show that the optical effects of ‘‘dusting’’ wavelength-sized hosts by microscopic grains can vary depending on the number and size of the grains as well as on the complex refractive index. Our computations also demonstrate the high efficiency of the new superposition T-matrix code developed for use on distributed memory computer clusters.