Greg Rusedski reached the second round of the Rotterdam Open on Monday with a straight-sets win over Czech Robin Vik.
Rusedski is ranked 43 in the world
Rusedski was always in control against the unseeded Vik winning 6-3 7-5, but admitted tennis was taking second place to his new daughter Scarlett.
"Tennis is not my main focus any more - it's all about my baby girl," he said. "That really changes your perspective, it's definitely a lifestyle change."
Tim Henman hopes to overcome a back problem before his match on Wednesday.
Henman, who faces Thomas Johansson, suffered the problem in Zagreb last month and was forced to pull out of last week's Marseille Open.
"It was frustrating to not be able to play in Marseille but I'm hopeful I'll be able to play in Rotterdam," he said.
Top seed Rafael Nadal has pulled out of the tournament with a thigh injury, joining a growing list of top players absent from the tournament.
World number one Roger Federer is also missing, along with Australian Open finalist Marcos Baghdatis, Ivan Ljubicic, Marat Safin and Sebastien Grosjean.
Rusedski, who faces Russian Nikolay Davydenko in the next round after the top seed beat Jan Hernych 6-3 6-3, praised rising star Andy Murray, who won his first ATP title in San Jose at the weekend.
Murray is now ranked 47 in the world, four behind Rusedski and seven behind Henman.
But the British number two insisted he was not looking over his shoulder.
"He's the one who is 18. Myself and Tim have had pretty successful careers, he's the one who is getting new experiences.
"It's great to have three of us - maybe more - competing near the top of the game. I'm pleased for him and hope he can be an example for more British young players."
French Open champion Nadal, ranked second in the world, said he hurt his thigh during last weekend's semi-final loss in Marseille to Arnaud Clement.
"The upper part of my leg began to play up during the third set. After not playing for four months due to my ankle injury, doctors advised me not to play this week.
"I have to be completely fit first, I want to give it all I've got on court."
Baghdatis injured his groin during training on site at the Ahoy arena while Federer and Ljubicic, winner and finalist last year, have already withdrawn.