As is well known, signed languages are characterized by a much more pervasive iconicity than verbal languages. Iconicity implies a tentative representation of some perceptible property of the denotatum. Visual representations of visual properties of the denotatum in signed languages play an important role when the process of the formation of the general concept is at issue. I suppose that they anchor the concept to certain specific visual properties, at the expense of both other nonvisual properties inherent in the denotatum and of other visual properties of the denotatum, not represented by the sign. An analysis of iconic signs of the Italian Sign Language (LIS) shows that visual properties of iconically represented denotata either possess an inherently deictic nature, pointing in the direction of specificity, or may have an extremely generic nature. In this latter case, the classificatory criterion based upon the configuration of the denotata creates classes of heterogeneous elements, that have in common only one property. The consequences of all this on the hierarchical organization of lexicon are far- reaching.