One of the Fed's most ardent hawks may have a way out for the doves.
In an exclusive interview with CNBC on Friday, Philadelphia Fed President Charles Plosser for the first time called for the Fed's current stimulus program, or quantitative easing, to be capped.
This would solve several problems for the QE supporters, he said, including the apparent inability to even discuss reducing the amount of QE without a major disruption in the markets that potentially worsens the economy.
(Watch: Plosser's 'plan B' for bonds)
When the Fed announced QE2, "we said we were going to buy $600 billion and then we're going to stop and see what the economy looks like and then make another assessment," Plosser said. "I'm actually leaning to believe maybe that's a better way to get us out of this box of fine-tuning and adjusting."
The Fed prompted major market disruptions twice in the last three meetings: It surprised markets in June by announcing a timetable for reducing QE and rocked them again in September when it defied expectations for tapering the asset purchases.
(Read more: By not tapering, Fed actually increased stimulus)
Plosser pointed out that the Fed ended both of its previous QE programs without such disturbances.