Peter Rusthoven, a former Harvard Law Review editor, sat quietly one day in a Washington law library scanning legal documents, trying to figure out what might have to be done if the president were under anesthesia.

For most 29-year-old lawyers, the effort would be purely academic. But at that moment, on March 30, 1981, President Reagan lay unconscious under a surgeon's knife a few blocks away.

And Rusthoven's boss, counsel to the president Fred F. Fielding, needed the information to brief Vice President George Bush in the event that Bush would have to step in.

Every legal problem affecting the presidency -- major scandal or trivial request -- is funneled to Fielding and his seven lawyers, a group he fondly refers to as "a great little law firm."

It is in many ways the most powerful little law firm in town. It does what law firms everywhere do for a big client: spot trouble and keep the client out of it, or, if that is not possible, pull the client out of trouble once he is in it.

The White House counsel reviews every speech Reagan gives, every bill he signs or vetoes, every announcement, every official action and every matter that might in some way have legal significance to Reagan and the office he holds.

Most of what the firm does is confidential. But in the past 3 1/2 years, Fielding or one of his lawyers has been involved in looking into, resolving, explaining, burying or dealing with problems and issues such as the selection of Supreme Court Justice Sandra Day O'Connor, the Environmental Protection Agency furor, the questioning about purloined Jimmy Carter documents that was dubbed "Debategate," and the propriety of top Reagan aide Michael K. Deaver's publishing a diet book.

The work can involve checking a speech on a domestic matter for a statement that might imply endorsement of something illegal. Or it can entail cautioning top staff members and the president not to discuss the trial of attempted assassin John W. Hinckley Jr., lest there be a repeat of President Nixon's offhand remarks about cult-murderer Charles Manson -- comments that sparked calls for a mistrial in Manson's case.

It can be "pretty heady stuff" for someone not long out of law school, concedes 29-year-old John G. Roberts Jr., another Harvard Law Review editor and a former clerk to Justice William H. Rehnquist.

"But whenever I begin thinking how important it all is, I reach into this pile here and pull out one of these." Requests Run the Gamut

"These" are what some in the office call "the dogs" -- the outlandish requests for the president's endorsement, for using his name or Nancy Reagan's or the presidential seal.

Roberts, who worked as an assistant to Attorney General William French Smith before joining Fielding in 1982, works on a number of broad legal questions, focusing primarily on constitutional issues and criminal justice matters.

But he also worked last week on a weighty matter regarding whether it was appropriate for a company selling white gloves to mention Nancy Reagan's name in its ads.

Despite their varied backgrounds, the lawyers on Fielding's staff share several characteristics, including a staunchly conservative political viewpoint and a passionate loyalty to President Reagan. They also share a trait that Fielding has made something of his trademark -- caution. Fielding screened his staff to make sure they were as careful and meticulous as he is.

"I want somebody who is careful," several staff members recall Fielding saying when they first talked nearly four years ago.

The staff also handles the countless letters from people asking Reagan to declare certain days national holidays in honor of a product, an event or a cause.

"You would not believe the things people dream up for the president to sponsor or endorse," says Fielding's deputy, Richard A. Hauser. Some requests are crass commercial pitches from hucksters. Some are letters from people convinced the CIA has put electrodes in their brains.

Others are reasonably worthwhile, often charitable requests from Reagan family friends or backers. Those have to be answered carefully.

Each administration brings in a new White House counsel's office. Fielding's staff, chosen initially from about 375 resumes submitted after the 1980 election, was selected in part to reflect the diverse nature of the work. Fielding Served Under Nixon

Fielding, 45, a deputy to John W. Dean III during the Nixon administration, assisted during the transition period after Reagan's election. Reagan asked the affable, soft-spoken Fielding to take the counsel's job in January 1981. Fielding said he gave up a six-figure income and a partnership in the D.C. office of a prominent Philadelphia law firm to take the job.

Hauser, 41, is the only other staff lawyer with counsel's office experience. He was there during the last year of the Nixon administration. A former assistant U.S. attorney in Florida and Justice Department attorney, Hauser was working in his own small, general practice law firm in Washington when Fielding called from California shortly after the 1980 election.

It was 2 a.m. in Washington when the call came, Hauser recalled recently. The job, as it was for Fielding, was a substantial pay cut, even at the $70,000 salary. But Hauser did not hesitate. "It was a chance to serve, to make a contribution to the president and the presidency."

Hauser, Fielding's alter ego and the only staff member who sits in when Fielding is not able to attend senior staff meetings, supervises the staff and spends considerable time on selection of local judges. His office, like Fielding's, is in the White House. The rest of the firm works in the Executive Office Building.

Senior associate counsel David B. Waller, 35, a former trial attorney in the Justice Department and a former associate in Washington's fourth-largest law firm, Hogan & Hartson, focuses on lawsuits involving the president or the White House, whether it be a question of how many television networks are part of the White House "pool coverage," suits involving the CIA's actions in Nicaragua or the firing of air traffic controllers.

Waller, like many on the staff, is in frequent contact with the Justice Department. "They are the big outside law firm" for the White House, Waller said. "We are the in-house counsel."

H. Lawrence Garrett III, 45, a retired 20-year Navy veteran, was a senior attorney at the Office of Government Ethics. He personally cleared about 1,000 executive-level presidential appointments in the early months of the administration.

It is Garrett who advises potential nominees, even the administration's top officials, as to whether their investments might pose a conflict of interest in their prospective jobs. "I like to practice preventative law," Garrett observed recently. "I do a lot of green-eye-shade stuff."

Early on, Garrett said, administration members would call "at the last minute, virtually from the airport," to get Garrett's advice on whether they could travel somewhere, take their spouses along or speak to an organization.

Garrett would have to explain that, legally, the organization could not pay for the trip, so the trip would have to be paid by the official's agency and the spouse could not go along. The trip, more often than not, was canceled.

Peter Rusthoven, 33, like Waller and Garrett, has been in the counsel's office since the early days of the administration. Unlike his colleagues, he was heavily involved in the 1980 Reagan campaign, serving as Indiana media director and a speech writer. He is the only one who makes no secret of his intention to return to Indiana, become involved in politics and probably run for office.

Rusthoven, an associate in a prominent Indianapolis law firm when Fielding called him shortly after the election, focuses mostly on reviewing speeches and working on complex constitutional questions, though he does his share of the "dogs" and some litigation involving the president.

Sherrie Cooksey, 31, came to Fielding's staff in June 1982 after 18 months in the White House lobbying office. She still does a fair amount of legislative work, but now from a legal standpoint. Cooksey, who formerly worked at the Federal Election Commission, is increasingly busy with questions involving federal elections laws.

Cooksey also works closely with Fielding on judicial appointments, something she did in the lobbying office. The difference now is that she focuses on whether someone should be nominated by Reagan; her successor in the lobbying office works on Senate confirmation.

"The whole job is to iron out or spot problems," Cooksey said in a recent interview, "to give legal advice to protect the president and the office of the presidency."

Wendell Willkie II, grandson of the Republican presidential nominee in 1940, a Rhodes Scholar and Harvard University graduate, is the newest member of the firm, arriving in February after serving as general counsel of the National Endowment for the Humanities. Willkie, 32, works in a number of areas, including international trade.

If people in the administration do not know what to do with something or have a seemingly insoluble problem, the first inclination is "send it to Fielding" and let the lawyers figure out a solution, Willkie noted. "This is damage control central."

The lawyers generally work the 12-hour days that are typical for private Washington attorneys, coming in on Saturdays. They usually work separately, reporting to Fielding through memos or during twice-weekly staff meetings. Most rarely see the president. Fielding is the only one with ready access and regular contact.

Frequently, though, they work as a team, especially during crises such as the EPA scandal, "Debategate" or the uproar over finding $1,000 in then-national security affairs adviser Richard Allen's safe. At such times the workload, as one former staff member put it, is "inhuman." Influence Has Been Great

The office of White House counsel has existed in various forms at least since the days of Franklin Delano Roosevelt. Some occupants wielded enormous influence with their bosses, not only in legal matters but also in formulating domestic and international policy, in writing speeches, in pushing legislation and in politics.

President Truman's counsel, Clark M. Clifford, was viewed by many observers as the quintessential president's lawyer. Others, such as President Kennedy's counsel, Theodore C. Sorenson: Ford's, Philip W. Buchen: and Carter's, Lloyd N. Cutler, exercised enormous influence with their bosses.

Fielding's position is not the same. He is not a longtime Reagan confidant, and he reports not to Reagan but to White House chief of staff James A. Baker III.

But Fielding's influence is considerable and has grown in the past four years. Fielding has been a "superb lawyer and invaluable adviser" to Reagan, Baker said in a recent interview. Many of Reagan's close advisers were not veterans in the ways of Washington. "Fred has been here before and knows where the traps are," Baker said.

In part for that reason, Fielding has gravitated, if not to the level of the "big three" -- Baker, Deaver and counselor Edwin Meese III -- or to the Cabinet level, at least to the inner circle of the top eight or so White House advisers.

Part of Fielding's staying power stems from his ability to conciliate, negotiate and get his way without offending. He is the consummate behind-the-scenes player.

"Fred is not a guy who would go out front and create controversy," says former associate attorney general Rudolph W. Giuliani, who worked closely with Fielding on judicial appointments. Fielding chairs a joint White House/Justice Department screening committee for all federal marshals, U.S. attorneys and judges.

Another key to Fielding's influence and that of his office is that "they play things very, very straight," Giuliani said. "They were also very valuable to Justice because when Justice disagreed with another agency's position you could talk to him like a lawyer and department heads would listen to his advice."

Even those who have been on opposite sides credit Fielding's group with being professional. "I would give them very high marks," former House counsel Stanley M. Brand, a staunch Democrat, said in a recent interview.

Brand, who participated in negotiations last year over congressional requests for White House documents involving the EPA scandal, called Fielding "a very easy guy to deal with" and "someone who has a great understanding of Washington and the way things work here."

Brand credits Fielding with "moving in at the 11th hour and negotiating an agreement with the House on how to handle the disclosure of certain key documents."

"They have evolved over recent years as lawyers for the presidency," Brand added, "and that is good for the institution." Office Power Has Grown

The power of the White House counsel's staff has always been tied to the counsel's relationship with the president.

But post-Watergate reforms, a heightened public concern about presidential power and ethics, and an increase in litigation in general have led to an increase in the size and influence of the counsel's office.

As a result, starting in 1974 with Buchen's eight-lawyer staff, the counsel's office has evolved into an institution to protect the presidency with a permanent set of duties and responsibilities whether or not the counsel is a close adviser to the president.

The office is now viewed within the administration as an indispensable participant, along with the Justice Department, whenever the president is named in a lawsuit, whenever a top aide has a potential conflict of interest, whenever questions arise involving elections laws and in a host of other matters.

Buchen and his staff prepared three 4-inch-thick notebooks concerning those issues. The books, which a former Buchen staff member called a "road map on what to expect," included information on the War Powers Act, executive privilege issues, legislative and pocket veto matters, the appointment process and ethics and conflict-of-interest matters.

The notebooks were passed on to the counsel's office during the Carter administration, updated a bit and then passed on to Fielding's office, where, with updating, Fielding says, he will pass them on.

"Our goal," Fielding said last week, "is to leave the institution of the presidency as strong as we found it, or stronger. Fortunately, my client feels as strongly as I do about that."