Englishman Fleetwood, runner-up at last year's U.S. Open, snared a pair of eagles from par-fives on his way to a six-under-par 66, while Bradley followed with a 68 as the pair wound up on nine-under 135 through two rounds at Bay Hill.
Earlier in the day, the event took another loss as former world number one Jason Day withdrew because of a back injury. "I really didn't know what to expect, but I'm very pleased with my score".
Rory McIlroy said Wednesday achieving a career Grand Slam at the Masters next month would be "awesome" for golf as he warms up for Augusta at this week's Arnold Palmer Invitational. Mickelson was able to get that one to the front of the green, and he two-putted from 30 feet to salvage a double bogey.
"Apart from (the 4th through 6th holes) I actually played quite well today", Leishman said.
Held at Bay Hill Club & Lodge, the 2019 edition of Palmer's annual tournament has a total purse of $9.1 million and a winner's share of $1.64 million, according to the Golf Channel.
The prestigious US PGA Tour event at Bay Hill will field six of the world's top 10 golfers and 13 of the top 20, despite eight-time event victor Tiger Woods withdrawing on tournament eve. "I hit it exactly how I wanted".
Phil Mickelson was back at Bay Hill for the first time in six years and was entertaining as ever.
Eight-time victor Tiger Woods returns to challenge some of the best golfers in the world such as Justin Rose, Rickie Fowler and defending champion Rory McIlroy.
"I'm three shots off the top 10".
Day told the PGA Tour that he had an MRI on Monday that revealed he has a tear in a disk in his lower back.
Quizzed by reporters after the round Day, who didn't play a practise round or the pro-am this week, said he had hoped the injury would settle down during the round but it hadn't.
"My back was sore when I was practicing from Tuesday to Saturday, and I was going to practice on Sunday, but I woke up and couldn't really walk or sit in the vehicle".
"I was on a dose pack to try get the inflammation out of it", he added, "and that didn't get any better".
Day was one of just three Australians to start the week, Aaron Baddeley the best of the remaining two after 18 holes with a 2-under 70 to be T15.
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