To keep the shaft clean?
Stop smearing chalk all over it. Sounds too simple, but seriously watch what you are doing. A little prevention goes a long way.
Look at your hands. If you have chalk all over them then I would suggest you are over-doing it.
Look at the rails or floor where you were standing when you chalked. If you can see chalk there, then you are over-doing it.
I also take a moment to wipe off my hands frequently. Carry a towel in your case. Wash it occasionally. Wipe off your cue when you get a moment too. It's not going to clean itself.
Same with the wrap.
When you are done shooting wipe the cue off with a very slightly damp cloth or an alcohol wipe.
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