The development of metal stable isotopes as tools in paleoceanography requires a thorough understanding of their modern marine cycling. To date, no Cu isotope data has been published for modern sediments deposited under low oxygen conditions. We present data encompassing a broad spectrum of hydrographic and redox regimes, including continental margin and euxinic (sulphide-containing) settings. Taken together with previously published data from oxic settings, these data indicate that the modern oceanic sink for Cu has a surprisingly homogeneous isotopic composition of about +0.3‰ (δ65Cu, relative to NIST SRM976). We suggest that this signature reflects one of two specific water-column processes: (1) an equilibrium isotope fractionation between soluble, isotopically heavy, Cu complexed to strong organic ligands and an isotopically light pool sorbed to particles that deliver Cu to the sediment, or (2) an equilibrium isotope fractionation between the same isotopically heavy ligand-bound pool and the particle reactive free Cu2+ species, with the latter being scavenged by particulates and thereby delivered to the sediment. An output flux of about +0.3‰ into sediments is isotopically light relative to the known inputs to the ocean (at around +0.6‰) and the seawater value of +0.6 to +0.9‰, suggesting the presence of an as yet unidentified isotopically light source of Cu to the oceans. We hypothesize that this source may be hydrothermal, or may result from the partial dissolution of continentally derived particles.