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In 1972, J. Becker [J. Reine Angew. Math. 255] discovered a sufficientcondition for quasiconformal extendibility of Loewner chains. Many knownconditions for quasiconformal extendibility of holomorphic functions in theunit disk can be deduced from his result. We give a new proof of (ageneralization of) Becker's result based on Slodkowski's Extended lambda-Lemma.Moreover, we characterize all quasiconformal extensions produced by Becker's(classical) construction and use that to obtain examples in which Becker'sextension is extremal (i.e. optimal in the sense of maximal dilatation) or, onthe contrary, fails to be extremal.

Quasiconformal extensions, Loewner chains, and the lambda-Lemma