Long-wavelength measurements reveal a paucity of ice in the Moon's polar craters. We have used a radio telescope at Arecibo Observatory, Puerto Rico, to map features of the lunar poles — some as small as 300 metres across — by collecting long-wavelength radar images that can penetrate several metres of lunar dust. We find that areas of the crater floors at the poles that are in permanent shadow from the Sun, which are potential cold traps for water or other volatiles, do not give rise to strong radar echoes like those associated with thick ice deposits in the polar craters on Mercury. Any lunar ice present within regions visible to the Arecibo radar must therefore be in the form of distributed grains or thin layers.