Skill-Biased Technical Change is one of the most prominent explanations for the rise in wage inequality in the United States over the last decades. However, the explanation is challenged for several reasons. In this paper, I propose an alternative type of technical change, where new technologies are initially adopted only by a fraction of firms (henceforth referred to as Successive Technical Change). I show that the implications of Successive Technical Change - in a heterogeneous firms model with search frictions - are in line with a broad set of stylized facts I derive from the Current Population Survey and the Economic Census of the United States. In particular, the model is consistent with the polarization of within-group wage distributions and the revenue distribution, the rise in the skill premium, and the increase of the firm size wage premium of college-graduates relative to the one of non-college-graduates. Perhaps the most interesting prediction of the model is that - depending on the state of the economy - a policy that fosters technology adoption at small and medium sized firms may decrease inequality.