ok are you ready for a total cross-connect noob question?

whats the proper and best way to remove wire thats already been punched down in a cross connect?

i need to flip a few phone lines and have decided that moving the wires on the cross connect will be the best way to go. (long story)

anyways, the only way i can see to get the wire out it to pull on it hard, which must be BAD lol.