Most morphological theories are concerned with possible words, just the way (generative) syntactic theories focus on possible sentence structures. This talk takes a different perspective and discusses *existing* words, in particular those that – for some reason or another – fall outside the active generative capacity. These are words like English hapless or laughter, whose building blocks are not independently available (*hap, *-ter), or whose structural pattern is synchronically unproductive (e.g. [X-le]V as in crumble, nestle or handle). Such words combine regularity and idiosyncrasy and therefore fall between all stools: between phonology and morphology, between lexicon and grammar, between storage and computation. Hence, they pose interesting theoretical challenges, which will be discussed with the help of a new approach, Relational Morphology (Jackendoff & Audring 2020).