I have to tell you I got a product in Vegas at APA nationals called "The Sleeve" from the owner of Billiard Engineering that surpasses uses as compared to a breaking sleeve.
This product can be used for breaking, or slide it down on the shaft for masse's, or jumping, or shooting off a rail, or metal part of a pocket to protect a cue. It is made out of plastic but won't scratch the cue, and can grip the cue with pressure as well.
Also can take the place of wearing a glove. Great product!!!
I usually keep it on my break/jump cue, but can easily take it to my player if I need it. $24.95