According to Gibrat’s Law of Proportionate Effect, the growth rate of a given firm is independent of its size at the beginning of the examined period. This paper investigates whether Gibrat’s Law holds for new entrants in a given industry: that is for new small firms in the early stage of their life cycle. The main finding is that in some (but not in all) selected industries in Italian manufacturing Gibrat’s Law fails to hold in the years immediately following start-up, when smaller firms have to rush in order to achieve a size large enough to enhance their likelihood of survival. Conversely, in subsequent years the patterns of growth of smaller firms do not differ significantly from those of larger ones, and the Law is therefore confirmed