Shahar Pe'er returned to winning ways on Tuesday, defeating Barbora Zahlavova Strycova 6-1, 6-3 to advance to the second round of the Luxembourg Open. The 22-year-old Israeli, ranked number 38 in the world, held her serve throughout the match and clinched the convincing victory after breaking Zahlavova Strycova (87) four times. In the second round, Pe'er will face Spain's Carla Suarez Navarro, ranked No. 32. Kim Clijsters also progressed to the second round in Luxembourg on Tuesday, beating Meghann Shaughnessy 6-2, 6-2 in her first singles match since winning the US Open last month. Â Meanwhile, Martina Hingis won't make a comeback to competitive tennis. The 29-year old Hingis, who retired after getting a two-year ban in 2007 for testing positive for cocaine, said Tuesday in an interview with L'Equipe that she is happy with her new life. "I've got a nice house, my four horses," Hingis said. "On the tour, I had no life." Hingis added that even without being tested positive, she likely would have retired. "If I had won the four Grand Slam tournaments, maybe I would have continued," she said. "But I was on downslope. And I was suspended for two years, and that was it." AP contributed to this report.