But, it was in 2002 that Stevenson moved up to No. 18 in the world. She had played during the European indoor season in 2001 and was the only American player to appear in Moscow in 2001 following the September 11 terrorist attacks. In 2002, prior to the European indoors, she lost to Monica Seles in the Tokyo quarterfinals 6–7(9), 6–7(9), and there were no breaks of serve until the tiebreakers. Alan Mills, the Tokyo referee and renowned Wimbledon referee proclaimed, "This is the finest women's serving match I have ever seen." Soon after, Seles and Stevenson were asked to serve aces for the American Heart Association, bringing awareness to heart disease. Stevenson served 100 aces in 2003. During the 2002 European indoors, Stevenson won her first doubles title with Serena Williams in Leipzig, Germany. She reached the quarterfinals of Filderstadt, defeating number one Jennifer Capriati. She was a finalist at Linz, beating two top ten players en route, including Capriati. Stevenson finished the year at 18, percentage points away from No. 17, Elena Dementieva.