Muller, the highest remaining seeded player in the tournament after top-seeded Michaella Krajicek was upset Monday, defeated Slovenian qualifier Andreja Klepac 6-2, 6-1.
Third-seeded Agnieszka Radwanska of Poland and fourth-seeded Frenchwoman Emilie Loit also posted straight-set wins Tuesday. Radwanska beat Mariya Koryttseva of the Ukraine 6-1, 6-4, and Loit beat Spain's Maria Jose Martinez Sanchez 6-4, 6-3.
Italian Karin Knapp upset fifth-seeded countrywoman Roberta Vinci 6-2, 2-6, 6-3. Also, Romanian qualifier Sorana Cirstea beat seventh-seeded Kaia Kanepi of Estonia 6-2, 6-4, and eighth-seeded Agnes Szavay of Hungary won 6-2, 6-1 over Romania's Ioana Raluca Olaru.