Abstract: Mereological atomism is the thesis that everything is ultimately composed of atomic parts. Typically, this thesis is characterized by an axiom stating, more simply, that everything has atomic parts. The present paper argues that the success of the standard characterization crucially depends both on how the notion of composition is related to the notion of sum and on how the notion of sum is initially defined. In particular, we put forward a novel definition of mereological sum such that: (i) provided no strong decomposition principle is assumed, it is not equivalent to extant definitions in the literature; (ii) can be used to claim that the standard characterization of atomism fails in that for something to have atomic parts is not sufficient for it to be be the sum of its atoms, and (iii) delivers a purely mereological distinction between structured and unstructured wholes [Joint Work with Alessandro Giordani, Catholic University of Milan].