Scotland's Martin Laird relinquished his overnight lead after a second-round points haul of seven at the Barracuda Championship in Nevada.
The 33-year-old tempered five birdies with three bogeys, leaving him on 22 points - two behind leader Greg Chalmers of Australia at the PGA Tour's only modified Stableford event.
England's Greg Owen - the other Brit to make the cut - is tied for 53rd.
The winner of the competition will earn £2.3m and an Open Championship spot.
Laird said it would be "great" to secure a place in the field at Royal Troon later this month.
He said: "It's always nice for me to go back to Scotland. The Open is my favourite tournament in the year."
The Barracuda Championship - formerly known as the Reno-Tahoe Open - is the only one on the PGA Tour to use a modified Stableford format, with eagles worth five points and birdies worth two.
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