The present invention is a combination light handle cover having flexible light handle cover performance in its grip part and semi-rigid light handle performance in its protective upper flange, where two snap fit connections are formed between the invention combination light handle cover and a rigid light handle which is adapted to be fixed rigidly to a surgical light or lamp. A lower snap fit connection is formed between lower female impressions (such as tabs) in the combination light handle cover at a relatively smaller diameter portion of the combination light handle cover in a zone between the grip part and the protective upper flange, which first female impressions snap fit to a lower extension ridge of the rigid light handle. An upper snap fit connection is formed between upper female impressions (such as tabs) in the combination light handle cover at a relatively large diameter portion of the combination light handle cover in a zone upon its protective cover, which second female impressions snap fit to an upper extension ridge of the rigid light handle, which upper extension ridge has a diameter much greater than that of the lower extension ridge.