The dependence of the number of clusters, N, and the average size of the clusters, [R], formed by nucleation and growth in the first stages of first-order phase transformations on the initial supersaturation, chi, is analyzed. The analysis is based on the numerical solution of a system of rate equations of classical nucleation theory describing this process. It is shown that in agreement with von Weimarn’s proposal for moderate values of the initial supersaturation these dependencies may be expressed in form of power laws ([R] proportional to chi(-p); N proportional to chi(q); p > 0, q > 0). However, considering larger intervals of the initial supersaturation, two distinct regions may be distinguished, characterized by different values of the exponents p and q. The results are of importance both from a theoretical point of view stimulating attempts to reconfirm the results by analytical methods as well as with respect to technological applications of nucleation theory, allowing one to draw conclusions on the initial dispersity of the evolving phase in dependence on the initial supersaturation.