Heinrich Layers, anomalously thick layers of ice-borne sediment in the North Atlantic ocean, have long been associated with abrupt climate changes in glacial times. However, there is still no consensus on either the exact amount of ice needed to transport this sediment or how such a large volume of ice could be produced. Using an iceberg model that includes sediment, we simulate the delivery of sediment to the North Atlantic during such an event. Our model assumes that sediment is uniformly distributed within the ice with a concentration of 4%. Unlike sediment models which assume that the sediment lies in a single layer, this model can carry sediment all the way from the western to the eastern North Atlantic. We use a variety of different estimates for the total volume of ice released to model the sediment layer thickness and we show that to best fit the observations (with a plausible range of ) of ice needs to be released. This is equivalent to a 0.04 Sv (, with a plausible range of 0.02–0.08 Sv) release of freshwater over the 500 yr of a typical Heinrich Event. This is a smaller flux of water than is required to show a significant impact on the global climate in most current “state of the art” GCMs.