In this article, I reconsider the diachrony of the Ancient Greek periphrastic construction of eimi‘I am’ with present participle by means of Bertinetto’s recently proposed model for the development of progressive grammatical morphemes (grams) (a process called ‘prog imperfective drift’). While Bertinetto’s proposal sheds new light on the diachronic development of the construction, at the same time the evidence from Ancient Greek brings to light the need for modification and further refinement of the model (most importantly with regard to the role of what I call the ‘stative’ aspectual function, next to the diachronic source(s) of the construction). I furthermore show that eimi‘I am’ with present participle never fully developed a (focalised) progressive function, which can be explained in terms of ‘constructional competition.’