We consider all atomic Bose-Einstein condensate held within an optical cavi
ty and interacting with laser fields. We show how the interaction of the ca
vity mode with the condensate can cause energy due to excitations to be cou
pled to a lossy cavity mode, which then decays. thus damping the condensate
. We show how; to choose parameters for damping specific excitations, and h
ow to target a range of different excitations to potentially produce extrem
ely cold condensates.