In recent years a number of researchers have argued that, in order to adequately explain contrast and its effects, phonology must be systemic: evaluation of a form cannot occur in isolation from unrelated contrasting forms, but must take such forms – what we call a ‘comparison set’ – into account. This presents a formal and empirical challenge for systemic approaches. This paper explores the comparison set within the general approach of dispersion theory, focusing on two matters: the ‘problem of infinity’ and idealisation. A further challenge for the theory, though one shared by many non-systemic approaches too, involves substantiating claims about perceptual distance that underpin the approach. Our discussion of the latter issue focuses on secondary palatalisation contrasts in onset versus coda position, with perceptual data from Irish. Our overall goal in this paper is to clarify the nature of these challenges and to outline our own approach to them.