It is often suggested that the Greenland ice sheet is a relict ice mass left over from the Ice Ages. In that case the ice sheet would not regrow to its present configuration under present-day climatic conditions if it were to melt away in a warmer climate, except for some residual mountain glaciers in the east. The most cited reasons for this alleged hysteresis are the height-mass balance feedback and the albedo-temperature feedback. Future climatic warming is expected to cause more melting on the Greenland ice sheet, resulting in an overall shrinking of the ice sheet. For a warming in excess of some 3°C, models predict that the surface mass balance will become negative such that the ice sheet can no longer be sustained and starts to gradually disintegrate. An intriguing question is whether there exist points-of-no-return once such a disintegration has set in beyond which complete removal of the ice sheet were to become irreversible, even if climatic conditions were to revert to present-day conditions. To investigate these issues, we have inserted a 3-D thermomechanical model of the Greenland ice sheet in the HadCM3 atmosphere-ocean general circulation model. Under constant 4xCO2 conditions, the Greenland ice sheet is found to disintegrate to less than 5% of its current volume within 3000 years. At different moments in time, we interrupt the melting process by inserting a 1xCO2 climate and let the ice sheet evolve to a new steady state. We also investigate the end member in which the ice sheet is entirely removed and bedrock topography has been uplifted. The original contribution of our approach is that precipitation and temperature patterns are allowed to fully interact with the changing topography and surface type of the Greenland continent.