We introduce explicit icebergs from a dynamic and thermodynamic iceberg model into an intermediate complexity climate model, which includes the coupled atmosphere-ocean system. This modeling approach allows iceberg meltwater to be injected into the ocean on the basis of thermodynamical considerations along the iceberg trajectories. Icebergs are seeded from known ice sheets in both hemispheres. Adding icebergs to the present-day climate model has a minimal impact, but during the Last Glacial Maximum (LGM), Atlantic overturning strength is reduced by a third, while producing a model state that is consistent with a steady state climate. We test the sensitivity of the model at the LGM to additional Heinrich event-scale fluxes of icebergs from three possible sources: Hudson Strait, the Gulf of Saint Lawrence, and the Norwegian Channel Ice Stream (NCIS). The sensitivity of the ocean is similar for all locations, with differences dominated by the length of the iceberg meltwater pathways to the main ocean convection region. The NCIS events result in more variability and a distinctly different, more northerly, salinity anomaly. We compare these results to a more typical modeling approach, whereby meltwater is injected directly into the ocean at the iceberg source locations, and find that these floods overestimate the oceanic response compared to the iceberg events. Our results suggest that 0.3–0.4 Sv of additional freshwater flux, either as icebergs or freshwater, is required to shut down the North Atlantic meridional overturning, a larger freshwater flux than sometimes suggested because of the localized nature of the release of the freshwater.