Is it possible to reuse a copper pipe's compression fitting?
If it hasn't been tightened many times, it should be okay to reuse.

Clean off the mating faces thoroughly and don't use tape, putty, or anything else.  And don't be gentle tightening:  The seal is formed by forcing the surfaces together and "bending" them to mate.

Even with threaded steel pipes, it can take a day or two for the tightened fittings to form a good seal and they can drip at first.  The essential observation is whether the drip rate slows hour by hour&mdash;if it does, it is probably okay and going to seal.

If it doesn't drip more slowly, try tightening a little more with water pressure applied until two consecutive small turns (1/8 turn) doesn't immediately decrease the drip rate.