In this paper we continue our analysis, begun in [S.M. Sakerin, R.F. Rakhimov, E.V. Makienko, and D.M. Kabanov, Atmos. Oceanic Opt. 13, No. 9, 754-758 (2000)], of the anomalous spectral dependence of the aerosol optical depth of the atmosphere, the important peculiarities of which are the following: a decrease in the UV spectral range with a minimum near 0.44 μm and a wide maximum in the range 0.6-0.8 μm; conservatism of the observed spectrum (and, hence, the aerosol microstructure) during 2.5 days. To explain the observed dynamics of the aerosol optical depth we considered the possible scenario of coagulation development of fine aerosol, which is in agreement with delay of the growth of the accumulative fraction. Direct and indirect data are presented on the existence and optical significance of a narrow fraction of medium-disperse particles (~0.3-0.6 μm). A possible mechanism of formation of this fraction is monodispersization of coarse aerosol due to gravitational sedimentation. Results of solution of the inverse problem are discussed for some atmospheric situations (Antarctica, Tomsk, Leningrad Region) which show that the narrow medium-disperse fraction is inherent to the global background aerosol (in the atmospheric column) and plays a dominant role in the formation of the anomalous spectral dependence.