In previous research, word–word compounds and stressed affix + word structures have been assigned to the same prosodic domain in Brazilian Portuguese (BP), on account of certain similarities in phonological behaviour (Silva 2010, Toneli 2014): both types of composite structures undergo vowel raising at the right edge of each element in the construction, and vowel sandhi processes between their elements. In this paper, I show that word–word compounds and stressed affix + word structures exhibit significant differences in stress patterns in BP, which supports their prosodization in two separate domains. While stressed affix + word structures are assigned secondary stress following the phonological word (PWd) stress algorithm, each element in word–word compounds behaves as an independent PWd with regard to the stress pattern that it exhibits. I thus propose that while stressed affix + word structures are recursively prosodized in the PWd domain, word–word compounds are prosodized in the composite group, the domain proposed by Vogel (2008, 2009) that immediately dominates the PWd and accounts for the prosodization of structures with compositional characteristics. The analysis reconciles two views on prosodic structure that are traditionally assumed to be mutually exclusive: the view that prosodic domains can be recursive (e.g. Inkelas 1990, Selkirk 1996) and the view that the prosodic hierarchy includes an additional domain specific to composite structures above the PWd (e.g. Vogel 2009, Vigário 2010).