Kristina Mladenovic moved into the Nottingham Open second round, while former champion Donna Vekic battled through on Wednesday.
Mladenovic, coming off a French Open doubles success, was too good for qualifier Magdalena Frech 7-5 6-2 at the WTA International tournament.
The eighth seed managed to break five times in her win, setting up a last-16 meeting with Australian Astra Sharma.
Vekic, the 2017 champion, overcame Dalila Jakupovic 6-2 6-7 (5-7) 6-0 in just under two hours.
After a second-set hiccup, the Croatian rushed through the third set, losing just 10 points to advance from a match moved indoors due to persistent rain in Nottingham.
On what was a good day for the seeds, Caroline Garcia thrashed Naiktha Bains 6-1 6-2, Maria Sakkari brushed past Heather Watson and Ajla Tomljanovic beat qualifier Danielle Lao.
At the Rosmalen Grass Court Championships in 's-Hertogenbosch, two-time runner-up Kirsten Flipkens upset fourth seed Lesia Tsurenko 7-6 (10-8) 7-5 in the second round.
There were also wins for qualifier Greet Minnen and Natalia Vikhlyantseva.