It also limits swelling by reducing blood flow to the injured area. Keep in mind, though, that you should never leave ice on an injury for more than 20 minutes at a time. Longer exposure can damage your skin. The best rule is to apply cold compresses for 20 minutes and then leave them off for at least 20 minutes. Compression limits swelling, which slows down healing.
Some people notice pain relief from compression as well.
An easy way to compress the area of the injury is to wrap an ACE bandage over it. If you feel throbbing, or if the wrap just feels too tight, remove the bandage and re-wrap the area so the bandage is a little looser. Elevating an injury reduces swelling. It's most effective when the injured area is raised above the level of the heart. For example, if you injure your ankle, try lying on your bed with your foot propped on one or two pillows.