Third seed Maria Sakkari was dumped out of the OEC Taipei WTA Challenger in the first round by qualifier Ashleigh Barty on Tuesday.
Naomi Broady, the second seed, was beaten on day one of the tournament and Sakkari also fell at the first hurdle when she went down 6-4 0-6 6-3.
Sixth seed Evgeniya Rodina never looked like making an early exit as she outclassed home contender Pei-Chi Lee 6-2 6-1, while Marina Erakovic, seeded eight, saw off Kyoka Okamura 6-4 6-2.
Former world number five Daniela Hantuchova's participation was cut short when she retired from her match against Ipek Soylu while trailing 4-2 in the final set.
There were no surprises in the Engie Open de Limoges, with fifth seed Sorana Cirstea brushing aside Amra Sadikovic 6-1 6-2.
Mandy Minella, the seventh seed, got past Dayana Yastremska 6-4 7-5 and eighth seed Stefanie Voegele only needed two sets to win her opening match against Mona Barthel.