The main aim of this article is to reexamine and argue against the existence of words with two main stresses which have been reported to occur in Guugu Yimidhirr (a Pama- Nyungan language, spoken in Queensland, Australia). Based on phonological evidence from patterns of clash avoidance and the distribution of secondary stress, it is claimed that in the alleged words with two main-stressed syllables, each syllable has a different metrical status. Only the initial one is main-stressed. The second is treated as an unstressed syllable by the metrical phonology of this language. The article also entertains and explores a tonal account in order to explain why some Guugu Yimidhirr words have been reported to bear two main stresses. Moreover, the article connects the discussion to “level stress,” a phenomenon similar to the Guugu Yimidhirr’s but found in some Mainland Scandinavian dialects. In contrast to previous analyses found in the literature to solve the puzzle posed by Guugu Yimidhirr double-headed words and Scandinavian “level stress”, this article finds no empirical support that motivates the weakening of the prosodic theory by either allowing recursion at the level of the Prosodic Word or by proposing the existence of disyllabic feet with both of their syllables stressed.