Top seed Amelie Mauresmo swept aside French compatriot Mary Pierce 6-4, 6-1 in the second round of the Antwerp Diamond Games tournament on Thursday.
"My game is becoming more and more aggressive but at the same time I am able to remain calm and focused," said Mauresmo, who meets Switzerland's Patty Schnyder in Friday's quarter-finals.
"I know that tennis can be disappointing but I am only thinking about the good things that it can bring," added Mauresmo, who often suffers from nervousness in big matches.
French Open champion and second seed Anastasia Myskina also advanced, but she was forced to dig deep to overcome France's Tatiana Golovin 6-3, 6-7, 6-4.
"It was a tight match," Myskina said. "But I expected no less. Tatiana is a very good player."
Myskina will be hoping for an easier contest in the last eight against Slovenian qualifier and doubles specialist Katarina Srebotnik, who saved five match points in her 4-6, 6-1, 7-6 victory over Russia's Anna Chakvetadze.
Earlier, Australian Alicia Molik, a quarter-finalist at last month's Australian Open where she beat Venus Williams, battled past Bulgarian Magdalena Maleeva 4-6, 6-2, 7-6.
The fourth seed next faces unseeded Czech Klara Koukalova, who eased into the last eight with a 6-4, 6-3
Williams and home favourite Kim Clijsters complete the quarter-final line-up with a highly-anticipated contest between former world number ones.
Clijsters is the defending champion but is using this tournament as a comeback event after a debilitating wrist injury has kept her sidelined for five months, causing her ranking to drop to number 87.
Despite playing well in the first two rounds, Clijsters's coach Marc Dehous rates third-seeded American Williams as the more likely to advance.
"Venus is the favourite. If I had to put money on someone tomorrow, I'd put it on her," Dehous said.
"But Kim will fight. She is very competitive and always gets better with the challenge. She can certainly raise her level against the best players, plus she really wants to play".