Mapping cultural influences and differentiating them from independent development is often problematic and, in many cases, has to be left undecided with the acceptance that further evidence may emerge. The squinch-supported dome and the lanterndecke ceiling are cases in point. Both are found in different regions of Eurasia during the first millennium and simple narratives of intercultural transmissions fail to explain adequately their chronology and distribution. Here, in the first of two papers, I concentrate on the former and its appearance in eastern Central Asia.1 I look at current scholarship to illustrate the issues with formulating a plausible narrative of transmission. This article is intended to raise questions and suggest ways forward rather than reach any conclusions, although I would argue that the most plausible hypothesis with the current evidence is that the squinch seen at Miran in eastern Central Asia is a case of architectural transmission from further west, most probably Bactria.