Abstract Movement is the locus of power in Minimalist grammars (MGs) but also their primary source of complexity. In order to simplify future analysis of the formalism, we prove that every MG can be converted into a strongly equivalent MG where every phrase moves at most once. The translation procedure is implemented via a deterministic linear tree transduction on the derivation tree language and induces at most a linear blow-up in the size of the lexicon.