The Greenland Ice Sheet (GrIS) is one of the most dominant orographic obstacles for atmospheric flow in the Northern Hemisphere. Within an idealized framework, we investigate the potential impact of a reduced Greenland topography upon precipitation, snow accumulation, and atmospheric circulation over the GrIS. Using the global atmospheric model ECHAM5-HAM at about 1° spatial resolution (T106) and with present-day climatological mean conditions, we perform four 16-year sensitivity experiments that are identical except for the height of the GrIS topography: one control simulation with the present-day Greenland topography, and three simulations with topographies reduced to 75%, 50%, and 25% of the present-day height. This simple reduction of the GrIS topography (as compared to realistic melt dynamics) leads to an overall increase in annual total precipitation and snow accumulation, composed of significant increases in eastern, northern, and central Greenland and decreases on the western slopes. In principle, this gain in snow accumulation raises the possibility of a negative feedback that would stabilize the height of the GrIS. However, this feedback is likely overcompensated by enhanced ablation (positive feedback), as surface air temperatures strongly increase with reduced topographic height. The analysis of changes in circulation patterns indicates that flatter topographies allow the atmospheric flow to penetrate farther inland, enabling precipitation in regions that are presently desert-like. Prominent circulation features change, in particular the all-season Greenland Anticyclone and wintertime Icelandic Low become weaker with lower topography.