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Fulla, Uppman, and Živný [ACM ToCT '18] established a dichotomy theorem for Boolean surjective general-valued constraint satisfaction problems (VCSPs), i.e., VCSPs on two-element domains in which both labels have to be used in a solution. This result, in addition to identifying the complexity frontier, features the discovery of a new non-trivial tractable case (called EDS) that does not appear in the non-surjective setting. In this work, we go beyond Boolean domains. As our main result, wedoi:10.4230/lipics.stacs.2019.52 dblp:conf/stacs/MatlZ19 fatcat:mxwjycnib5hwlhfs3wkvs3upte