Abstract. Based on a comprehensive set of fission-fragment distributions measured in low-energy fission, the even-odd staggering in the fission-fragment element yields is investigated. The well-established evolution of the global even-odd effect with the fissioning system is found to be only a partial aspect of the even-odd structure. Indeed, it is shown that the global even-odd effect varies systematically with the mean asymmetry of the fission-fragment distribution, and that the general increase of the even-odd staggering with asymmetry depends on the fissioning system. Thus, the dependency of the even-odd effect with the fissioning system is accredited in part to the asymmetry evolution of the charge distribution, and not solely to the dissipated energy as it has been done earlier. This interpretation is strongly supported by data measured in inverse kinematics, which cover the complete fission-fragment charge distribution and include precise yields at symmetry. The relevance of the ordering parameter for the description the even-odd effect in fission-fragment yields as a general property is explored.PACS numbers: 24.75.+i, 25.85.Ec, 25.85.Jg