Just like most varieties of West Germanic, virtually all varieties of German use a construction in which a cognate of the English verb do (standard German tun) functions as an auxiliary and selects another verb in the bare infinitive, a construction known as do-periphrasis or do-support. The present paper provides an Optimality Theoretic (OT) analysis of this phenomenon. It builds on a previous analysis by Bader and Schmid (An OT-analysis of do-support in Modern German, 2006) but (i) extends it from root clauses to subordinate clauses and (ii) aims to capture all of the major distributional patterns found across (mostly non-standard) varieties of German. In so doing, the data are used as a testing ground for different models of German clause structure. At first sight, the occurrence of do in subordinate clauses, as found in many varieties, appears to support the standard CP-IP-VP analysis of German. In actual fact, however, the full range of data turn out to challenge, rather than support, this model. Instead, I propose an analysis within the IP-less model by Haider (Deutsche Syntax-generativ. Vorstudien zur Theorie einer projektiven Grammatik, Narr, Tübingen, 1993 et seq.). In sum, the do-support data will be shown to have implications not only for the analysis of clause structure but also for the OT constraints commonly assumed to govern the distribution of do, for the theory of non-projecting words (Toivonen in Non-projecting words, Kluwer, Dordrecht, 2003) as well as research on grammaticalization.