Graeme McDowell takes on Korean YE Yang at the WGC-Accenture Match Play Championship in Tucson looking to move ahead of Tiger Woods in the world rankings.
Either McDowell or Luke Donald could be world number three by Sunday night after they both made it into the last 16.
Donald, the ninth seed, faced another Italian job. After knocking out Ryder Cup team-mate Edoardo Molinari, he now faces 17-year-old Matteo Manassero.
McDowell, meanwhile, takes on YE Yang knowing that even if he loses he will move ahead of Woods - beaten by Thomas Bjorn on Wednesday - in the world rankings.
"If someone told me at some point in my career I would be number three in the world I'd be proud of that fact," said the Northern Irishman.
"I'm perhaps a better golfer than Tiger in the last 12 months, but he's definitely the greatest player that's ever lived I think and it would be nice to slip past him for a little while."
The US Open champion found himself being asked as many questions about 21-year-old compatriot Rory McIlroy as he did about his own victory over England's Ross Fisher.
McIlroy was crushed 8&7 by an inspired Ben Crane and only Canadian Stephen Ames has ever suffered a bigger defeat in the event. Ames lost 9&8 to Woods five years ago.
"I can't really get my head around that right now," commented McDowell. "This golf course sets up for the Rory McIlroy-type driver of the ball and Ben Crane is not really known for length, but a guy who is just holing everything on you can wear you out.
"I think Rory's looking inside as to how he can continue to get better. Everyone's career is going to have setbacks and this is just a mini-setback.
"As long as he can learn and put what he learns to good use it's only a matter of time in my opinion until he becomes a phenomenal player and a prolific winner.
If Donald wins the title McDowell will have to be among the semi-finalists to take the world number three spot, while to go to number one Martin Kaymer has to reach the final.
Kaymer has another chance to take the world number one spot this weekend following Lee Westwood's second round defeat to American Nick Watney.
The German, who needed two extra holes to get past Justin Rose, now takes on Hunter Mahan.
Dove Mountain is considered a course for big hitters, but Ian Poulter won last year and Donald's style - Woods once described him as a "plodder" - is serving him well so far.
"I can't overpower this course - I have to take the long route round," he said. "But if I can play my golf and play consistently that puts the pressure on my opponents and they try to force the issue a bit."