British pair Dan Evans and James Ward both lost in straight sets in round two of the Aegon Championships at Queen's Club.
Evans, the British number two, was beaten 6-2 6-3 by South Africa's seventh seed Kevin Anderson.
British number three Ward later went down 7-5 6-3 to Bulgarian fourth seed Grigor Dimitrov.
Andy Murray begins his title defence against Frenchman Paul-Henri Mathieu on Wednesday.
Evans, who beat Austria's world number 51 Jurgen Melzer in the first round on Monday, struggled to make an impact against the big serving of 6ft 8in Anderson and went out in 65 minutes.
An early break of serve put the South African in charge and when he moved 4-2 ahead in the second set, there was no way back for the Briton.
"I didn't get a chance to play tennis, really," said world number 139 Evans, who is targeting a good performance at Eastbourne next week to improve his ranking.
"Next week is a pretty big week. Smaller draw, more ranking points. That's the week you're going to pick up your points."
Evans, 24, added that he was confident he could see off the potential threat of Aljaz Bedene, the Slovenian-born player who hopes to qualify for Britain next year, to his Davis Cup place.
Evans is currently ranked seven places below Bedene, but believes he is "a better player" than the London-based 24-year-old.
"I have nothing against him. I just wouldn't do it personally," Evans added. "He's a nice guy. He's played Davis Cup for a different country. I just don't think it would be right if he played Davis Cup for our country."
Ward set up a meeting with Dimitrov after a 7-5 6-4 win against Slovenia's Blaz Rola on Monday.
The 27-year-old produced a gallant display against the world number 13 but was undone after losing his serve at crucial moments in each set.
Unseeded Australian Marinko Matosevic caused an upset as he beat ninth seed Marin Cilic, the 2012 champion and 2013 runner-up, 6-4 6-4.
Matosevic was asked afterwards what he thought about Murray's decision to work with Amelie Mauresmo, and said: "For me, I couldn't do it since I don't think that highly of the women's game. But his mum coached him, and she did a great job with him."
Mauresmo arrived at Queen's Club on Tuesday ahead of starting work as the new coach of Wimbledon champion Murray.
The 34-year-old Frenchwoman's appointment, initially for the grass-court season, was announced on Sunday.
British number one Murray practised at Queen's on Tuesday morning with Bedene. Dani Vallverdu, Murray's long-time assistant coach, oversaw the session along with fitness trainer Matt Little.