The build-up of the Greenland Ice Sheet (GrIS) from ice-free conditions is studied in an ice sheet model (ISM) driven by fields from an atmospheric general circulation model (GCM) to demonstrate the importance of coupling between the two components. Experiments where the two are coupled off-line are augmented by one where an intermediate ice sheet configuration is coupled back to the GCM. Forcing the ISM with GCM fields corresponding to the ice-free state leads to extensive regrowth which, however, is halted when the intermediate recoupling step is included. This inhibition of further growth is due to a Föhn effect of moist air parcels being lifted over the intermediate ice sheet and arriving in the low-lying Greenland interior with high temperatures. This demonstrates that two-way coupling between the atmosphere and the ice sheet is essential for understanding the dynamics and that large scale conditions cooler than those of today may be necessary for the GrIS to regrow to the present volume