In　this　paper,　we　propose　a　variation　of　weak　covariance　named　as　non-singleton　covariance,　requiring　that　changing　the　worth　of　a　non-singleton　coalition　in　a　TU　game　affects　the　payoffs　of　all　players　equally.　We　establish　that　this　covariance　is　characteristic　for　the　convex　combinations　of　the　equal　division　value　and　the　equal　surplus　division　value,　together　with　efficiency　and　a　one-parameterized　axiom　treating　a　particular　kind　of　players　specially.　As　special　cases,　parallel　axiomatizations　of　the　two　values　are　also　provided.　©　2018　EDP　Sciences,　ROADEF,　SMAI.