Recent remote sensing data strongly suggest that deposits of ice occur in p
ermanently shadowed regions at the lunar poles. Clementine, by providing th
e first contiguous coverage of the Moon, has enabled the production of an i
llumination map of the south pole. This map shows the extent of the areas o
f permanent darkness during winter in this region as well as identifying pl
aces on the lunar surface that receive illumination for more than 50% of th
e lunar day: The permanently dark areas are prime candidates for locations
of ice deposits while regions that are illuminated for anomalous periods ar
e possible sites for lunar bases. In this paper we study in detail the illu
mination history during a lunar day of some of these sites. While we find n
o area that receives permanent illumination, we do find two areas, only 10
km apart, which collectively receive sunlight for over 98% of the time.