The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with the mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, i.e. the method separates the ill-posedness of the problem from the measurement errors. Neither an artificial discretization of the size distribution nor an initial size distribution are required, radii for the evaluation of the size distribution may be freely selected. The real analysis of the measurements is only a matrix vector operation. © 1998 IOP Publishing Ltd.