The paper contributes to the long-running debate, in Cognitive Linguistics, about the polysemy of spatial particles of verticality, notably English over, and especially focuses on the contrastive dimension with Italian. The study resumes and expands on preceding work presented at the International Conference on Language, Communication and Cognition (Brighton, August 2008) and is part of a larger project on the English-Italian mapping of spatial particles. The research highlights that the English and the Italian repertoires of spatial particles of verticality are asymmetric and that the semantic networks of over and su/ sopra (along with closely related compositional sets), in particular, involve asymmetric and complex sense extensions which result in less predictable options in translation. From the empirical point of view, reference is made to corpora data, while on the theoretical point of view, the study makes reference to the framework of Lexical Complexity (see Bertuccelli Papi and Lenci 2007; Masi 2010) as a rationale for a principled organisation of the cross-linguistic mapping. Other works and models, too, are taken into account as a starting point for the comparison, notably the Principled Polysemy Network model by Tyler and Evans (2003). Spatial particles, in fact, are among the most problematic topics to be mastered by Italian learners of the English language. The ultimate goal of the research is indeed to highlight guidelines for developing a ‘pedagogical contrastive grammar’ of the English-Italian particles at issue (and correlated teaching material), also building on, and developing ideas from Tyler and Evans (2004), Evans and Tyler (2005), and Tyler (2008).