It's Alan Greenspan's swan song. The Federal Reserve raised interest rates last week, as expected. The overnight Fed funds rate went from 1 percent, the lowest since the late 1950s, to 1.25 percent. Over the next year or two, most economists expect the Fed to continue increasing rates; the idea is to contain inflation without smothering the economic recovery. This seems to be Greenspan's last big move on the nation's money and credit markets. His term at the Fed ends in January 2006, and present law bars reappointment. If this final maneuver succeeds, it could secure a dazzling record.

Look back. He arrived in 1987 after Paul Volcker had drubbed double-digit inflation. Under Greenspan, the Fed has faced many problems: the stock market crash of 1987; weak banks in the early 1990s; the 1997-98 Asian financial crisis; the stock market and tech bubbles of the late 1990s; and the aftermath of Sept. 11. But there have been no calamities. The two recessions (1990-91 and 2001) were mild. Inflation has declined -- from 4.4 percent in 1987 to 1.9 percent in 2003 -- and incomes have risen. From 1987 to 2003, gross domestic product increased by 61 percent and the number of jobs by 25 million.

He's made it look easy. Compared with earlier threats, the present challenge seems tame. For three years, the Fed has aggressively combated a weak economy with cheap credit. The Fed funds rate has been below 2 percent since late 2001, and at 1 percent since June 2003. Now the recovery seems firm. In the past year gross domestic product growth has averaged 4.8 percent. Job growth has resumed. On the other hand, unemployment remains high enough to mute pressures for big wage gains, which -- being the largest cost for business -- might spill over into higher prices. The economy seems strong enough to tolerate higher interest rates and weak enough to permit rates to rise slowly.

But appearances may deceive. We now have a new book from a former Fed governor that provides a glimpse of Greenspan's Fed. It's much messier than advertised. Nominated by President Bill Clinton, Laurence Meyer served from 1996 to 2002. Before that, he taught economics at Washington University in St. Louis and ran a widely known forecasting firm. His book "A Term at the Fed'' isn't a kiss-and-tell tale; it focuses on economic issues. Still, it offers fascinating insights.

By Meyer's account, Greenspan and the Fed often fly by the seats of their pants. Despite a staff of 220 economists armed with computer models, the Fed is regularly surprised. In 1996 and early 1997, unemployment (then close to 5 percent) was declining. By the models, tight labor markets should have increased inflation. But inflation was dropping. "We had never seen anything like this before," Meyer writes. There were other surprises. The Fed didn't foresee the Asian financial crisis, the extent of the stock market bubble or the 2001 recession. Meyer doesn't criticize the Fed staff, which he thought excellent. But there were limits to what could be predicted.

So judgment counts -- and one man's counts most. On paper, Greenspan casts just one vote in 12 on the Federal Open Market Committee, the key decision-making group. (The other votes are the six other Fed governors and five presidents of the regional Federal Reserve Banks.) But in practice, things are different. "While this is not written anywhere," notes Meyer, "the chairman is expected to resign if the [FOMC] rejects his policy recommendation." To Meyer, efforts to craft a consensus were haphazard. The Fed was a "rather lonely place to work." Governors met mostly in formal committees; he rarely saw Greenspan in private.

The result is that a lot depends on how one man copes with uncertainty. In 1996 and early 1997, Greenspan resisted higher interest rates. Based on skimpy statistics, he judged that computers were improving business productivity (output per hour worked). Companies could cut costs; they didn't have to raise prices. Although better statistics later confirmed Greenspan's view, the pressure was always to accept it. Today's situation is not entirely dissimilar, because uncertainties abound.

For starters, low interest rates sustained a housing boom and, quite possibly, caused a bubble in real estate values. The Fed faces two dangers in raising rates: raising them too slowly, and raising them too rapidly. If the Fed funds rate -- the only rate the Fed actually controls -- increases too slowly, then inflation might worsen. Higher inflation could then push up other interest rates, because lenders expect to be compensated for the eroding value of their money. Already, the consumer price index is higher than expected. It was up 3.1 percent in the past year, though "core inflation" (without food and energy prices) was up only 1.7 percent. But raising the Fed funds rate too rapidly might stall the economic expansion. In 1994 higher rates did just that. Either way, home building and housing prices are vulnerable.

Greenspan needs to walk a thin line. Just because the odds are on his side is no guarantee. Can he? History -- and his legacy -- await the answer.