This article is concerned with aspects of lexicalization in the history of English from the perspective of Construction Grammar (CxnG). I show how constructional approaches can account for both grammaticalization and lexicalization within a unified framework, basing my argument around the two kinds of input to lexicalization which Brinton & Traugott (2005: 96) identify: syntactic constructions and word formation patterns. In lexicalization, linguistic forms that initially participate in an abstract schematic macro- or meso-construction, become idiosyncratic micro-constructions, whereas in grammaticalization an idiosyncratic micro-construction comes to participate in a more schematic meso- or macro-level construction.The main part of the paper is devoted to a discussion of the evolution of what Taylor (1996) has described as possessive compounds, such as driver's license, in the history of English. I specifically consider how the CxnG framework can explain the development of form-meaning mismatches, conventionalization, and the loss of internal constituency, in lexicalization. The data suggest that a constructional approach can account for the two stages of lexicalization (grammatical to lexical, less lexical to more lexical) in a way parallel to the two stages of grammaticalization (lexical to grammatical, less grammatical to more grammatical).