But, when conditions eventually cleared beside Lake Michigan, the world number one – a shocking joint 78th out of 80 in last week’s world championship – scored a one-under-par 71.

It left him only three behind early pacesetters Bubba Watson and Italian Francesco Molinari.

A week ago Woods trailed by 10 after day one, so there was the measure of the improvement.

Yet the round looked as if it was going to be much, much better.

Woods, needing a top-15 finish to have a chance of qualifying automatically for the Ryder Cup, birdied three of his first four holes and shared the lead at that point.

Dropping back to level par with bogeys on the 15th – his sixth – the long second and short seventh was a big disappointment, but he raised his morale again with a closing birdie.

That left him feeling far better about things than Padraig Harrington, who looks likely now to require one of Colin Montgomerie’s three wild cards after managing only a three-over 75.

“I was very confident going out, but was a little bit too aggressive,” said the Dubliner, who now concedes that in terms of the Ryder Cup he made some mistakes with his schedule earlier in the season.

“But I’m still trying to win the tournament. Eight under won here last time (that was Vijay Singh in 2004) and I don’t see why it won’t be again – but the cut will be an issue tomorrow.”

Harrington’s biggest error came on the short 17th, his eighth, where he pulled a four-iron onto the rocks by the water and double-bogeyed.

Woods commented: “I hit the ball pretty good and I felt like I had control - my trajectory was nice and I’ve not had in a while.

“I just need to keep improving every day.”

Molinari is already on course for a cup debut at Celtic Manor in October and he birdied two of the last three to match the 68 of left-hander Watson.

One behind were Australian Jason Day and Americans Charles Howell, Ryan Moore and Matt Kuchar.

Scot Martin Laird was one further back and compatriot Stephen Gallacher shot 71, but Paul Casey and Luke Donald handed in 72s – Casey despite chipping in twice. Both were for pars and one followed a near-shank off the 17th tee.

Ian Poulter had a triple-bogey seven on the 15th, his sixth, but birdied two of the next three and then came back from another dropped shot at the fourth with back-to-back birdies.

The later starters included Montgomerie, who had received a vote of confidence from players and from the European Tour after the spotlight had been put on his private life for the second time this year.

Richard Hills, Europe’s Ryder Cup director, said: “We have absolute confidence in Colin as Europe’s captain and we look forward to him standing on the first tee at Celtic Manor when the 2010 Ryder Cup starts exactly 50 days from now.”

Montgomerie, doubtless cheered by support at a difficult time, even went to one under with a birdie on the 13th, his fourth.