This paper explores the diachronic semantics of two almost-approximators in Hungarian: majdnem (‘almost-M’) and szinte (‘almost-S’). I will show that there is a neat division of labour between these two: majdnem is an intensional approximator (possible worlds) whereas szinte is a scalar approximator (precision standards), a situation similar to that observed in Russian (čut’ ne and počti). I will show that this can be straightforwardly derived from the grammaticalization trajectories of the two approximators: majdnem derives from the adverb majd ‘soon’ (and the expletive negator nem ‘no’) and szinte derives from an adverb originally meaning ‘by outward appearance, superficially’. These two processes both exhibit semantic bleaching and the semanticization of originally pragmatically inferred information. With the help of corpus data, I will also track and explain in terms of competing grammars how, in certain environments, majdnem is in the process of crowding szinte out.