Havret leads Johnnie Walker
Montgomerie, who has six wins and two ties in singles matches from his eight Cup appearances, probably needs to win this week to convince Faldo to pick him. He is 20th in the standings after a poor summer.
"This was OK. One over is by no means out of this tournament," said the 45-year-old Scot, who expects to be Ryder Cup captain when the event is played here in 2014.
Havret, who won the Scottish Open at Loch Lomond last year, started at the 10th hole and made three birdies before dropping his only shot at No. 1.
Then he birdied Nos. 4-6 and took a two-stroke lead over Christian Cevaer, Paul Broadhurst, Robert Rock and Gary Orr.
Dougherty was a protege of Faldo when he was younger and badly wants to play on his team at Valhalla. Dougherty's mother died this year and he has struggled with his form since.
"I decided I'd do my best to make the team because she always wanted me to play the Ryder Cup," he said. "I've always wanted to play in Nick's team. I'm very tired but as long as I give it everything and leave everything out on the course this week, I'll be satisfied."
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