Melbourne:Once again Serena Williams started slowly and finished solidly as she moved to within three victories of a "Serena Slam". Serena, the French and US Open and Wimbledon champion, beat Eleni Daniilidou 6-4, 6-1 on Monday after a first set in which she gestured in exasperation over some misses. Her sister Venus Williams waltzed into the quarterfinals on Sunday with a 6-3, 6-2 victory over Australian Nicole Pratt. Serena's quarterfinal opponent will be American compatriot Meghann Shaughnessy, who saved five break points in the final game to beat Elena Bovina 5-7, 6-2, 6-4. "That's a great win for (Shaughnessy)," Williams said. "OK, that's two Americans in the quarterfinals so one of us is guaranteed to get to the semis." Also in the quarterfinals is her elder sister Venus, who lost to Serena in last year's final three Grand Slam events. Meanwhile, Rainer Schuettler made the most of 2002 runner-up Marat Safin's withdrawal by reaching the final eight with a 6-3, 6-4, 1-6, 6-3 victory over American James Blake. Hot match Williams played the last match on center court before organizers suspended play on outside courts, citing temperatures of 35 Celsius (95 Fahrenheit) and high humidity. They had the option of closing the roof over center court. "It's hard to breathe," said Williams, who sat gulping air during the changeovers. "But it's OK, I like the heat." Williams, who missed the Australian Open with an injury last year before winning three straight majors, has struggled at the beginning of three of her four matches here so far. Her serve was broken twice in the first set but she broke three times, helped by eight double faults by the 20-year-old Daniilidou, a Greek seeded 18th. Then Williams settled down, reducing her errors from 21 in the first set to six in the second. First quarterfinal Shaughnessy, a 23-year-old American who's seeded 25th, reached the quarterfinals of a Grand Slam event for the first time by winning her 11th straight match to start the year. Before the Australian, she won a warmup tournament in Canberra. Serving for the match against Bovina, a US Open quarterfinalist last year, Shaughnessy saved break points with an error by the 19-year-old Russian, a service winner, an overhead smash, an inside-out forehand and an ace. After another service winner, she finished the 2-hour, 19-minute match when the 20th-seeded Bovina netted a backhand serve return. Schuettler advances Schuettler gained a free pass into the fourth round when Safin withdrew with a wrist injury after falling in an earlier match. Schuettler, a 26-year-old German who had never reached a Grand Slam quarterfinal before, rebounded from early service breaks by Blake in the first two sets. In the final set, the two traded service breaks in the fourth and fifth games, and Schuettler gained the key break in the sixth when Blake double-faulted. Schuettler finished with a forehand down the line that Blake couldn't handle at the net. The 23-year-old Blake, playing in a Grand Slam event's fourth round for the first time, had 35 errors, compared with 19 by Schuettler. "When you're playing for something that's really important, the quarterfinal of a Grand Slam, it hurts," Blake said. "I learned something. You can't play the same tennis in the second week as you can in the first." Henin scrapes through Justine Henin-Hardenne just about crawled into the quarterfinals, writhing with leg cramps near the end of her three-set victory over Lindsay Davenport. "I thought I was going to die," Henin-Hardenne said. "But I played with heart and just went for it." After being treated with ice on the court, the Belgian defeated the once top-ranked Davenport 7-5, 5-7, 9-7 in 3 hours, 13 minutes. On Monday, Henin-Hardenne withdrew from the doubles to rest for her singles quarterfinal. She next plays 63rd-ranked Virginia Ruano Pascual of Spain, a 6-3, 6-3 winner over 62nd-ranked Denisa Chladkova of the Czech Republic. Meanwhile, fourth seed Kim Clijsters of Belgium had an easy win over Amanda Coetzer of South Africa, 6-3, 6-1.