The commonly employed concept of describing measured size-dependent particle number concentrations of ambient aerosols as the sum of lognormal distributions is analysed critically. The starting point is the idea that it is generally desirable to assign a single distribution function to each source of aerosol particulate matter. The problems encountered in determining the most appropriate function are illustrated by considering the very pronounced changes in shape produced by converting number concentration distributions n(D) of particles with diameter D to mass concentration distributions m(D). It is shown that m(D) can exhibit a pronounced peak even if n(D) is a function that decreases monotonically with increasing particle size. The basic considerations are applied to generate much more realistic fit functions for the contribution of the accumulation and the dust mode to measured particle number concentrations. Depending on the particle size, the improved fit functions may differ from the lognormal fit by up to several orders of magnitude. The contribution of fugitive dust to the mass concentration can be made to agree with predicted concentrations as well as with PIXE data for the concentration of crustal elements in samples collected with impactors. (C) 2003 Elsevier Ltd. All rights reserved.