* Call for more clarity from both ends of policy spectrum
* Fed last month dropped very specific rate guidance
ROCHESTER, Minn./PHILADELPHIA, April 8 (Reuters) - The Federal Reserve needs to be more specific about what economic conditions would prompt it to raise interest rates from current rock-bottom levels, a pair of top Fed officials normally at loggerheads on policy said on Tuesday.
A third, meanwhile, warned that the Fed should be sure not to withdraw monetary policy accommodation before the economy is ready.
The call for more clarity on rate-hike plans comes just weeks after the Fed jettisoned a very specific promise to keep rates low until unemployment falls below 6.5 percent, and instead said rates would stay low for a considerable time beyond the end of its massive bond-buying program, which should wind down later this year.
After the policy-setting meeting, Fed Chair Janet Yellen briefly roiled markets when she suggested that "considerable time" might mean around "six months."
"We would be better off having more of a collective vision as a committee to what the change in conditions would have to be that would lead us from ending the asset-purchase program to raising rates," Narayana Kocherlakota, president of the Federal Reserve Bank of Minneapolis, told reporters after speaking to the Greater Rochester Chamber of Commerce.
"Unless we communicate as a group about what those conditions are, then we face this instability that two words in a press conference, or two words in a speech or an answer to a senator can end up moving financial markets participants' vision of what we are trying to do with policy."
Kocherlakota's lone dissent against the Fed's policy decision last month marks him as the central bank's most dovish member. On Tuesday, he said the Fed should consider lowering the target for its main policy rate, already between zero and a quarter of a percentage point, even further, and could cut the interest rate its pays banks on funds they keep at the Fed.
Those ideas do not appear to have broad support at the Fed.
A PLEA FOR MORE PRECISION
Still, on Tuesday, one of the Fed's most hawkish policymakers joined Kocherlakota in calling for better rate guidance.
After the Fed said last month it would look at a wide range of factors to judge when the economy is strong enough for rates to rise, some investors and economists have kept busy developing "economic dashboards" and complex data "webs" to keep tabs on how close to healthy the economy may actually be.
"It was an important step," the hawkish chief of the Philadelphia Fed, Charles Plosser, said of the new Fed rate guidance. "And I'd like to see us ... refine that language, make it clearer as to what exactly we mean by that. ... That will be a tricky task, but I think we can make some progress on that ... (and) be more precise about it."
The timing of the first rate increase, which will probably come next year, will be "all about the data," Plosser said. The central bank is "not even close to withdrawing support prematurely."
Speaking at a separate event in Washington, Charles Evans, president of the Federal Reserve Bank of Chicago, voiced that very concern.
"One of the big risks is that we withdraw our accommodative policies prematurely," he said during a panel discussion at the International Monetary Fund.
(Reporting by Ann Saphir in Rochester, Minnesota, and Jonathan Spicer in Philadelphia; Editing by Jan Paschal)