How to tighten the connection between a camera adapter and a microscope ocular tube?

I have a camera adapter which has a metal tube which fits into a microscope ocular tube to allow taking photographs of the microscope's views through a point-and-shoot camera. My problem is that the connection isn't tight enough, leaving some wiggle room for the camera to move around and become off-center. By wrapping several layers of adhesive tape around the adapter tube, the fit becomes more snug, however the tape is not very precise and still allows the camera to become off-center. I intend to try using some heat shrink tubing around the adapter tube to see if that yields a better fit, but I don't have confidence that it will work very well. Does anyone have any other ideas to solve this problem?