Reusing corks is a very bad idea. Firstly it's damaged, secondly it's been contaminated at a microscopic level both inside & out. ALWAYS use new corks.
Regards, GF.
nope, I don't even like to recork the bottle they came out of with them. If the corkscrew went through the other side (tends to happen with the short corks you find) and you store the bottle on its side in the fridge, it will leak out the hole from the corkscrew.