Kevin Anderson's challenge at the Winston-Salem Open ended in disappointment after he was ousted by Sam Querrey.
James Ward is the last Briton left in the US Open qualifying draw after Dan Evans and Daniel Smethurst both bowed out.
World number one Serena Williams has been named as top seed for the US Open, which starts on Monday.
Andy Murray needs to ‘step up’ at the US Open, according to John McEnroe.
John Isner booked his place in the third round of the Winston-Salem Open with a straight-sets victory over Bradley Klahn.
Simona Halep suffered a blow to her US Open preparations as she was dumped out of the Connecticut Open on Tuesday.
Britons Naomi Broady and Dan Cox both suffered defeat on the opening day of US Open qualifying.
British men's number one Andy Murray has been seeded eighth for this year's US Open.
Bradley Klahn beat Noah Rubin to set up a second-round encounter against top seed John Isner in the Winston-Salem Open.
Caroline Wozniacki overcame a slow start to reach the second round of the Connecticut Open