The Federal Reserve begins one of its regular policy meetings Tuesday. But this one will feel anything but routine.

For the first time in months, the outcome of the meeting is genuinely in question. The Fed must decide whether to begin pulling back on the rate at which it pumps new money into the economy. It has been buying $85 billion in bonds using newly created money for the past year, but it might be ready to start closing the spigot. It would be the most concrete step the Fed has taken toward trying to wind down its aggressive interventions to support economic growth.

And it occurs against an almost surreal backdrop, with the president facing a decision over whom to appoint to succeed Ben S. Bernanke as chairman of the institution when his term is up Jan. 31. Former Treasury secretary Lawrence H. Summers was the front-runner but took his name out of the running Sunday amid opposition from Senate Democrats.

Against these complex issues, the central bank will announce its policy move Wednesday afternoon following a two-day meeting, along with its leaders’ economic projections. What is probably Bernanke’s next-to-last quarterly news conference will follow.

Apart from the theatrics surrounding the Fed succession — a topic Bernanke will avoid at the news conference if the recent past is a guide — the chairman faces an unusually delicate task.

In June, when the Fed met and Bernanke signaled that the central bank would probably begin tapering bond purchases later in the year, it caused a sell-off on global markets as investors began to prepare for a world with less money-printing emerging from the powerful U.S. Fed.

Assuming the Fed begins its long-telegraphed “taper” of bond purchases, Bernanke will face a core question: Why is the central bank taking its foot off the accelerator of growth at a time when measures of job growth and consumer spending have shown signs of slowing and inflation has been quite low?

One possible answer that many analysts have put forth is that the Fed will slow the pace of its bond purchases only modestly, reducing them, say, from $85 billion a month to about $75 billion. That would allow it to assess the effects on markets and have more time to see how the economy is evolving before acting further.

“We suspect the statement will make clear that the FOMC [Federal Open Market Committee] will decide on the need of further tapering at each meeting, and future policy steps will remain highly data dependent,” Annalisa Piazza of Newedge Strategy said in a research note.

Several Fed officials have expressed uneasiness about the economic side effects of the billions of dollars in bond purchases in recent months. But the central bank also has tried to separate the end of “quantitative easing” from the decision to raise interest rates. In other words, it wants markets to understand that the end of the bond purchases does not mean that a rate increase is imminent.

“If we are correct that tapering is a done deal, then the remainder of the meeting’s communications efforts will likely be an exercise in convincing the market that tapering does not necessarily lead in a straight line to a tightening of monetary policy,” said Michael Feroli, chief U.S. economist at JPMorgan Chase, in a research note.