The broken bracelet puzzle

One of my favorite puzzle books as a kid was Perplexing Puzzles and Tantalizing Teasers, by Martin Gardner. It had fun "real life" type problems (how can you drive an 11-foot-9 truck under a bridge with 11-foot-8 clearance?) and it introduced me to palindromes ("Straw? No, too stupid a fad. I put soot on warts.")

Here's another "real life" puzzle: a person brings four pieces of a broken bracelet to a jeweler and asks him to repair it. The jeweler says he charges $1 for each link he cuts apart and welds together again. "Since I have to cut and weld four links, the job will cost you four dollars." But the customer correctly tells the jeweler he can make the bracelet by cutting and welding only three links. How?