I have a lovely ring that my jeweler said is not a good candidate for resizing, so I used a piece of 18-gauge half round dead soft wire to fix it.
Depending on how much size needs to be corrected (and because you will probably do this while it is on your finger), I would use 20-gauge half round half hard wire. If you want the wrap to be symmetrical in length, take a piece that is about 6½" long, then fold it in half on an angle (with the domed side out). Place the fold over the center of the shank, and wrap toward each side. When it fits more comfortably, trim the ends, use a file to smooth them, and press them inside.
Answer contributed by Dale "Cougar" Armstrong