Coax cable issues.

I recently upgraded my modem for a faster speed. I was sent a new Coax cable along with the new modem. I want to continue to use my current coax cable, but it does not fit my new modem. It's too loose and I noticed, the conductor (cooper piece) is slimer then the new one that came with the modem. I do know want to remove my current cable because the line is running under my floor and through my basement. Is there some kind of adapter I can use that will assist me. I thought these coax cables were universal, but I guess it is not.