The article describes the contrastive possibilities of alignment of high accents in three Romance varieties, namely, Central Catalan, Neapolitan Italian, and Pisa Italian. The Romance languages analyzed in this article provide crucial evidence that small differences in alignment in rising accents should be encoded phonologically. To account for such facts within the AM model, the article develops the notion of "phonological anchoring" as an extension of the concept of secondary association originally proposed by Pierrehumbert and Beckman (1988), and later adopted by Grice (1995), Grice, Ladd, and Arvaniti (2000), and others to explain the behavior of edge tones. The Romance data represent evidence that not only peripheral edge tones seek secondary associations. We claim that the phonological representation of pitch accents should include two independent mechanisms to encode alignment properties with metrical structure: (1) encoding of the primary phonological association (or affiliation) between the tone and its tone-bearing unit; and (2), for some specific cases, encoding of the secondary phonological anchoring of tones to prosodic edges (moras, syllables, and prosodic words). The Romance data described in the article provide crucial evidence of mora-edge, syllable-edge, and word-edge H tonal associations. (Contains 24 figures and 22 footnotes.)