THOUSAND OAKS, California, Nov 27, 2012 (AFP) - Global governing bodies The Royal & Ancient and the US Golf Association were expected to announce a decision on Wednesday that could see a significant rule change in putting, perhaps a ban of "anchoring" putters on the body.
Last year, Bradley became the first player to win a major with a putter anchored on his midriff at the PGA Championship.
He was swiftly followed by Simpson at this year's US Open, and Ernie Els at the British Open.
Australia's Adam Scott used a chest-high broomstick putter as he narrowly failed to win his first major at the British Open.
If a new rule is proposed or enacted, it likely would not go into effect until 2016, when golf's rules are next scheduled to be updated.
Simpson, preparing to play in this week's World Challenge unofficial event hosted by Tiger Woods, said Tuesday he was ready to cope with whatever decision is handed down.
"I don't know what their definition of 'anchoring' is going to be," Simpson said, noting that US pro Matt Kuchar plays with a long putter that he holds against his forearm but which isn't anchored like a pendulum to his body.
"First of all, I think we've got to get a definition out," Simpson said, declining to be drawn into debate on whether a rules change would be "fair".
"I've been working with the short putter now for a couple of years," added the American, who said he switched to the belly putter in his college days in a bid for more consistency. "I'm not worried. I expected this day to come."
Bradley, who said in China earlier this month that he would do "whatever it takes to protect myself and the guys on tour," said Tuesday that the assumption he meant legal action was premature at least.
"I never said the world 'sue'. I never said 'legal action'. Somehow it got twisted around into that," Bradley said.
"I have total respect for Mike Davis and the USGA," added Bradley. "They are doing what they think is best for the game and I respect that. That doesn't mean I'm happy with the decision, but I respect what they're trying to do."
Like Simpson, Bradley said he was reserving his response until he actually hears what the R&A and USGA have to say.
But he said he believes it's not just the major victories prompting golf's rule-makers to act, but the increased use of long putters by youngsters coming into the game.
"Personally, I don't see why that's a huge negative," Bradley said. "But I would imagine that they're more worried about the younger guys than the guys kind of in the twilight of their career."
Long putters have been used in golf for more than 20 years, first gaining prominence on the 50-and-over tour now called the Champions Tour.
Rocco Mediate became the first player to win a PGA Tour event using a long putter anchored on his body in 1991, and Paul Azinger did so in 2000.
Plenty of influential voices have been raised against anchoring.
Els was among the opponents of belly putters back in 2004, only reluctantly turning to one to try to iron out his putting woes.
He has since said it requires skill to use effectively, but such greats as Tom Watson and Arnold Palmer have said an anchored putter does not produce a true golf stroke.
That's also the position of 14-time major champion Woods.
"I just believe that the art of putting is swinging the club and controlling nerves. And having it as a fixed point, as I was saying all year, is something that's not in the traditions of the game," Woods said Tuesday.
"We swing all other 13 clubs. I think the putter should be the same. It should be a swinging motion throughout the entire bag."