The amount of information (types of solutions, accuracy and moments of the solution) about tropospheric rural aerosol size distribution that can in theory be obtained from backscattered measurements, without using any additional information about the anticipated solution, has been discussed. In practice, additional assumptions (constraints) must be used to solve for aerosol size distribution. The inferred solution reflects those assumptions and is therefore not objective. The quality of the solution depends on the applicability of the constraints to the given problem. A library of pseudo-empirical functions is used to form a set of orthogonal basis functions. It is assumed that any unknown aerosol size distribution may be constructed from a linear sum of these basis functions. The problem then becomes one of solving for the unknown coefficients of the basis functions. A solution with a smoothing constraint and a positivity constraint has been developed. Results of the method, when backscattered radiation is used as measurements, are presented. Discussion on the limitations of the method and the effects upon the solution of the different assumptions that are used is given. Some possible uses of the solution are considered.