This paper investigates the prominence patterns of nominal triconstituent compounds in English. The standard assumption for such NNN compounds is that the branching-direction is responsible for stress assignment. In left-branching compounds, i.e. those of the structure [[NN] N], the leftmost noun is assigned highest prominence whereas in right-branching compounds, i.e. [N [NN]], the second noun is the most prominent one (so-called ‘Lexical Category Prominence Rule’, e.g. Liberman and Prince, Linguistic Inquiry 8: 249–336, 1977). This assumption has hardly ever been tested empirically in more detail. Using acoustic data from several hundred pertinent compounds from the Boston University Radio Speech Corpus, we found that the predictions of the Lexical Category Prominence Rule are borne out for the majority of the data. However, a considerable number of compounds do not behave as predicted and violate the Lexical Category Prominence Rule. The analysis of the aberrant cases shows that prominence assignment to triconstituent compounds is governed also by factors other than branching. These factors are suggested to be the same as those responsible for the assignment of leftward vs. rightward stress to biconstituent compounds.