Sloane Stephens was comfortably beaten by 151st-ranked Kristina Kucova at the Monterrey Open on Tuesday.
Madison Keys had not played on tour since September, but the American looked in good shape as she began her season in Doha.
The cold weather in Paris was an issue for Victoria Azarenka but nothing could spoil Simona Halep's birthday celebrations.
Former world number one Andy Murray made his grand slam return at the US Open and will get another shot at Roland Garros.
Patricia Maria Tig was the beneficiary as Eugenie Bouchard failed to see out victory in the Istanbul Cup final on Sunday.
Eugenie Bouchard looks to be putting her tennis career back on track, with an impressive effort in Istanbul this week bringing reward.
Eugenie Bouchard beat Svetlana Kuznetsova for the first time to reach a third quarter-final of 2020 in Istanbul.
Number one seed Svetlana Kuznetsova awaits qualifier Eugenie Bouchard in the second round in Istanbul.
Aliaksandra Sasnovich was knocked out at the last-32 stage of the US Open, and she returned to winning ways at the Istanbul Cup.
Two-time grand slam champion Simona Halep took less than an hour to sail into the last four of her first tournament for six months.