According to the widely accepted Lexical Category Prominence Rule (LCPR), prominence assignment to triconstituent compounds depends on the branching direction. Left-branching compounds, that is, compounds with a left-hand complex constituent, are held to have highest prominence on the left-most constituent, whereas right-branching compounds have highest prominence on the second of the three constituents. The LCPR is, however, only poorly empirically supported. The present paper tests a new hypothesis concerning the prominence of triconstituent compounds and suggests a new methodology for the empirical investigation of compound prominence. According to this hypothesis, the prominence pattern of the embedded compound has a decisive influence on the prominence of the whole compound. Using a mixed-effects generalized additive model for the analysis of the pitch movements, it is shown that all triconstituent compounds have an accent on the first constituent irrespective of branching, and that the placement of a second, or even a third, accent is dependent on the prominence pattern of the embedded compound. The LCPR is wrong.