An algorithm of phrase structure building is proposed within the bare phrase structure framework. The algorithm is rooted in the idea that applications of Merge–the operation that combines syntactic objects–should not change the set of basic relations (in particular, c‐command) in the existing structure, what Chomsky (2000) terms “Least Tampering.” Under the proposed algorithm, this idea translates into a requirement that Merger must take place at the root of the tree/phrase marker when possible. As a result, the algorithm forces (base‐generated or moved) structural adjuncts to be Merged postcyclically. Three empirical consequences of the proposed algorithm are discussed: (1) constructions involving raising across the experiencer (e.g., John seems to Mary to be smart) are shown not to be problematic for the Minimal Link Condition (cf. Chomsky 1995b); (2) a novel account of Adjunct Island effects (Huang 1982) is proposed; and (3) a principled analysis of approximative inversion in Russian is offered.