In this paper, we extend to complex sentences the proposal that the notion of clause in Align/Match constraints related to the syntax-prosody mapping of the intonational phrase should be determined in each language (and each construction) by making reference to the highest syntactic phrase whose head is overtly filled by the verb (or verbal material) (Hamlaoui & Szendrői 2015). We propose that while root-clauses have a privileged status from the syntax-toprosody mapping perspective, all clauses are equal in the prosody-to-syntax mapping. In the spirit of the Minimalist Program (Chomsky 2005), we bring in extragrammatical motivation for the proposed mapping principles from parsing and learnability. This allows us to account for the fact that, whereas in many languages like Bàsàá (Bantu) and Hungarian (Finno-Ugric), only root clauses normally map onto intonational phrases, additional intonational phrase edges can be found under the pressure of high-ranked prosodic, processing or information-structural requirements. This is the case with Hungarian embedded foci and Bàsàá embedded topics where, we argue, embedded ι edges are meant to satisfy StressFocus and AlignTopic, respectively. In languages where embedded clauses seem to map onto their own intonational phrases more generally, such as Japanese or Luganda, further independent constraints should be evoked.