Models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) show substantial biases in the deep ocean that are larger than the level of natural variability and the response to enhanced greenhouse gas concentrations. Here, we analyze the influence of horizontal resolution in a hierarchy of five multi-resolution simulations with the AWI Climate Model (AWI-CM), the climate model used at the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, which employs a sea ice–ocean model component formulated on unstructured meshes. The ocean grid sizes considered range from a nominal resolution of ∼1∘ (CMIP5 type) up to locally eddy resolving. We show that increasing ocean resolution locally to resolve ocean eddies leads to reductions in deep ocean biases, although these improvements are not strictly monotonic for the five different ocean grids. A detailed diagnosis of the simulations allows to identify the origins of the biases. We find that two key regions at the surface are responsible for the development of the deep bias in the Atlantic Ocean: the northeastern North Atlantic and the region adjacent to the Strait of Gibraltar. Furthermore, the Southern Ocean density structure is equally improved with locally explicitly resolved eddies compared to parameterized eddies. Part of the bias reduction can be traced back towards improved surface biases over outcropping regions, which are in contact with deeper ocean layers along isopycnal surfaces. Our prototype simulations provide guidance for the optimal choice of ocean grids for AWI-CM to be used in the final runs for phase 6 of CMIP (CMIP6) and for the related flagship simulations in the High Resolution Model Intercomparison Project (HighResMIP). Quite remarkably, retaining resolution only in areas of high eddy activity along with excellent scalability characteristics of the unstructured-mesh sea ice–ocean model enables us to perform the multi-centennial climate simulations needed in a CMIP context at (locally) eddy-resolving resolution with a throughput of 5–6 simulated years per day.