A large amount of literature on conceptual abstraction has investigated the differences in contextual distribution (namely “contextual variability”) between abstract and concrete concept words (“joy” vs. “apple”), showing that abstract words tend to be used in a wide variety of linguistic contexts. In contrast, concrete words usually occur in a few very similar contexts. However, these studies do not take into account another process that affects both abstract and concrete concepts alike: “specificity, that is, how inclusive a category is (“ragdoll” vs. “mammal”). We argue that the more a word is specific, the more its usage is tied to specific domains, and therefore its contextual variability is more limited compared to generic words. In this work, we used distributional semantic models to model the interplay between contextual variability measures and i) concreteness, ii) specificity, and iii) the interaction between the two variables. Distributional analyses on 662 Italian nouns showed that contextual variability is mainly explainable in terms of specificity or by the interaction between concreteness and specificity. In particular, the more specific a word is, the more its contexts will be close to it. In contrast, generic words have less related contexts, regardless of whether they are concrete or abstract.