The recognition of irony is a challenging task in the domain of Sentiment Analysis, and the availability of annotated corpora may be crucial for its automatic processing. In this paper we describe a fine-grained annotation scheme centered on irony, in which we highlight the tokens that are responsible for its activation, (irony activators) and their morpho-syntactic features. As our case study we therefore introduce a recently released Universal Dependencies treebank for Italian which includes ironic tweets: TWITTIRÒ-UD. For the purposes of this study, we enriched the existing annotation in the treebank, with a further level that includes irony activators. A description and discussion of the annotation scheme is provided with a definition of irony activators and the guidelines for their annotation. This qualitative study on the different layers of annotation applied on the same dataset can shed some light on the process of human annotation, and irony annotation in particular, and on the usefulness of this representation for developing computational models of irony to be used for training purposes.