Top seeds Petra Kvitova, Caroline Wozniacki and Kiki Bertens all secured a place in the second round of the Luxembourg Open.
Kvitova, the Czech world number 11, progressed with a 7-5 6-0 win over Su-Wei Hsieh of Chinese Taipei.
Dane Wozniacki beat Madison Brengle 6-2 6-2, while Bertens saw off Annika Beck of Germany 6-4 6-4.
Sixth seed Misaki Doi, though, is out after the Japan player was defeated 6-1 6-2 by Lauren Davis.
Johanna Larsson, the Swedish number eight seed, beat Pauline Parmentier 6-4 6-2, while Kristyna Pliskova is also through after she came from behind 3-6 6-3 6-4 against Oceane Dodin.
In Tuesday's late match, Sabine Lisicki, the German who reached the 2013 Wimbledon final, came through in three sets against Viktorija Golubic 6-3 3-6 6-2.
At the WTA Kremlin Cup event in Moscow, sixth seed Barbora Zahlavova Strycova suffered an early exit as the Czech player was beaten 6-4 1-6 6-2 by Ana Konjuh.
Seventh-seeded Russian Anastasia Pavlyuchenkova, though, is through after she beat Katerina Siniakova 7-6 (7/2) 5-7 7-5.
Elsewhere, Serbia's Jelena Jankovic, a semi-finalist in Hong Kong, is through after beating Jelena Ostapenko 6-3 6-3.
Alize Cornet will take on top seed Svetlana Kuznetsova in round two after the Frenchwoman defeated Shelby Rogers 7-6 (8/6) 6-3.
Australian Daria Gavrilova beat Lucie Safarova 6-2 6-2 to secure her place against number two seed Carla Suarez Navarro.
Source: PA
