Abstract In Icelandic there are two different types of modifiers within compounds, inflected and uninflected, and the inflected modifiers appear to be peripheral to the uninflected ones. In this article, it is proposed that this is an effect of compounding being required to combine elements of the same type or size. The inflected modifiers, containing more structure than the uninflected ones, cannot be merged at the same level as uninflected modifiers. This article also explores two other issues of domainhood within the compound. One being the establishment of domains for morphophonological processes, where it is proposed that the boundaries of morphophonological domains are determined by the edge of the extended projection of the root. The second one being that of special meaning, where it is shown that exocentric compounds with inflected modifiers have exclusively non-compositional meaning, whereas exocentric compounds with uninflected modifiers could have either compositional or non-compositional meaning.