Top 10 players Elena Dementieva and Patty Schnyder both won in straight sets to reach the second round of the Porsche Grand Prix in Germany.
Dementieva beat Zuzana Ondraskova of the Czech Republic 6-2 6-4 while Schnyder got the better of Serbian teenager Ana Ivanovic 6-1 6-2.
Russian Anastasia Myskina was also among Tuesday's winners.
Kim Clijsters can take the world number one spot from Maria Sharapova who is ruled out with a muscle injury.
Australian Alicia Molik, who has managed only one win since going down with a virus in April, lost 6-3 6-3 to Nathalie Dechy of France.