@ Advocatus Diaboli
When constructing this tool, I had also some worst case scenarios in mind. One scenario was about centering a very thin and, if you like, a pre domed cue tip with small dia (like some snooker or carom tips).
In such a case the inside of the tool gives you the easy possibility to reduce distance resp. to “lift” the thin cue tip so that it can be clamped.
So, this tool can manage thin tips.