Seeds Kristina Mladenovic and Daria Gavrilova opened their Volvo Car Open campaigns with wins, while Misaki Doi crashed out in the first round.
French 11th seed Mladenovic accounted for Tatjana Maria in straight sets in Charleston on Monday.
Despite tallying seven double faults, Mladenovic posted a 6-4 6-3 win over her German opponent in the first round.
Australian 12th seed Gavrilova advanced to the second round but she needed three sets to get past Zarina Diyas.
Gavrilova saw off Diyas 6-1 1-6 6-3 in one hour, 43 minutes.
Sabine Lisicki - the German 15th seed - also progressed beyond the first round with a 6-4 6-3 victory against Irina Falconi.
Doi was not so fortunate, upstaged by Kateryna Bondarenko in three sets.
The 16th seed claimed the opening set before Bondarenko rallied to win 4-6 6-3 6-1.
In other results, Danka Kovinic defeated Cagla Buyukakcay 6-1 6-3, Caroline Garcia was beaten 6-4 2-6 7-6 (7-3) by Irina-Camellia Begu and Christina McHale fell to Lourdes Dominguez-Lino 2-6 6-4 6-1.
Lara Arruabarrena beat Shelby Rogers 6-4 3-6 6-4, Laura Siegemund overcame Patricia Maria Tig 6-3 3-6 6-3 and Alison Riske prevailed 6-3 6-2 against Frances Altick.
Mirjana Lucic-Baroni was a 6-2 6-1 winner over Shuai Peng, Elena Vesnina was too good for Cindy Burger 7-5 6-2, Jana Cepelova rallied to beat Anastasija Sevastova 4-6 6-4 6-1, while Sesil Karatantcheva went down to Ana Konjuh 6-3 6-3.