There are many exact theoretical methods to simulate light scattering by small particles, but only a few of them, including in the first turn the Extended Boundary Condition Method (EBCM), allow one to perform calculations usually required in practical tasks, i.e. to take into account size, orientation and so on distributions of (simple model) scatterers. Importance of these methods caused by their wide applications was stimulating long time investigations of their applicability ranges. We report recent results of the analysis of EBCM-like methods. It is confirmed that the methods give a convergent solution (i.e. are mathematically correct) everywhere under the known conditions of validity of the Rayleigh hypothesis. Convergence of these methods used to calculate only the far-field characteristics of the scattered field (cross-sections, scattering matrix, etc.) occurs under a weaker condition. These general conditions are applied to the particular cases of spheroidal and Chebyshev particles as well as particles with sharp edges, and numerical results confirming the conclusions of our theoretical analysis are presented.