Warsaw, apr 30 Although Daniilidou provided stern competition, Mauresmo found the match a valuable experience as she tested her fitness.
As well as having to default her Australian Open quarter-final against Fabiola Zuluaga in January, she recently withdrew from the Charleston event because of continuing problems with her back.
She has even changed her service technique, not only to make it more effective but to ease the strain on her back.
In other second round matches, third seed Vera Zvonareva beat Lenka Nemeckova 6-1, 6-3, and ninth seed Francesca Schiavone set up a meeting with Mauresmo by overcoming Elena Bovina 6-2, 6-3.
Fourth seed Svetlana Kuznetsova needed just 40 minutes to overwhelm Vera Douchevina 6-0, 6-1, sixth seed Silvia Farina Elia struggled before getting the better of Polish wild card Marta Domachowska 6-4, 4-6, 6-4, and Magdalena Maleeva will meet Venus Williams after upsetting seventh seed Patty Schnyder 5-7, 6-2, 6-3.


Bureau Report