Traditional approaches to verbal periphrasis (compound tenses) treat auxiliary verbs as lexical items that enter syntactic derivation like any other lexical item, i.e. via Selection/Merge. An alternative view that has received much attention in recent years is that auxiliary verbs are not base-generated but rather inserted in a previously built structure (i.a. Bach 1967; Embick 2000; Arregi 2000; Cowper 2010; Bjorkman 2011; Arregi and Klecha 2015). Arguments for the insertion approach to auxiliaries include their last-resort distribution and the fact that, in many languages, auxiliaries are not systematically associated with a given inﬂectional category (the "overﬂow" distribution discussed in Bjorkman 2011). In this talk, I will argue against the insertion approach. First, I will demonstrate that the overﬂow pattern and last-resort distribution follow from Cyclic Selection (Pietraszko 2017) – a Merge-counterpart of Cyclic Agree (Béjar and Rezac 2009). And second, I show that the insertion approach makes wrong predictions about compound tenses in Swahili, a language with overﬂow periphrasis. Under the approach advocated here, an auxiliary verb is a verbal head selected and externally merged as a speciﬁer of a functional head, such as T. It then undergoes m-merger with that head, instantiating an external-merge version of Matushansky's (2006) conception of head movement.