Rhesus rhadinovirus (RRV) is currently the closest known, fully sequenced homolog of human Kaposi sarcoma-associated herpesvirus. Both these viruses encode complement inhibitors as follows: Kaposi sarcoma-associated herpesvirus-complement control protein (KCP) and RRV-complement control protein (RCP). Previously we characterized in detail the functional properties of KCP as a complement inhibitor. Here, we performed comparative analyses for two variants of RCP protein, encoded by RRV strains H26-95 and 17577. Both RCP variants and KCP inhibited human and rhesus complement when tested in hemolytic assays measuring all steps of activation via the classical and the alternative pathway. RCP variants from both RRV strains supported C3b and C4b degradation by factor I and decay acceleration of the classical C3 convertase, similar to KCP. Additionally, the 17577 RCP variant accelerated decay of the alternative C3 convertase, which was not seen for KCP. In contrast to KCP, RCP showed no affinity to heparin and is the first described complement inhibitor in which the binding site for C3b/C4b does not interact with heparin. Molecular modeling shows a structural disruption in the region of RCP that corresponds to the KCP-heparin-binding site. This makes RRV a superior model for future in vivo investigations of complement evasion, as RCP does not play a supportive role in viral attachment as KCP does.