It was quite a coup: The most private of Washington museums -- the Phillips Collection -- recently wooed Henry Kissinger onto their new "council."

The council is a way of easing the Phillips' small family board into expansion. "Our endowment doesn't do what it used to do," says Laughlin Phillips, director of the Collection. "With inflation, we can't get by on what we used to."

That's a problem at almost all of Washington's cultural institutions. And that's why the board game -- the competition for and recruitment of desirable trustees -- is being played more and more seriously these days as money gets tighter. Every museum or musical group would like to score as big as the Corcoran did a couple of years ago with its acquisition of multimillionaire Dr. Armand Hammer, who has art and money and enjoys giving them away.

That's why the Washington Performing Arts Society was so pleased last week to announce that Jean Sisco -- head of a Washington-based consulting firm and board member of several large corporations -- had become president of its board.

And that's why newcomers to Washington have been besieged by requests. When Vicki and Smith Bradley (an heir to the R.J. Reynolds tobacco fortune) arrived in 1976, "i was getting called by every board in town," said Vicki Bagley. "It was hard to sift through." She eventually joined the board of the National Symphony Orchestra.

When Elizabeth Taylor arrived here as the wife of Sen. John Warner (R.Va.) the boards went after her. "She's a movie star, so people think she can produce movie stars for benefits," said one veteran observer of the board game. "And we all have to have benefits.

Wolf Trap Farm Park, donated by Catherine Shopuse, got Taylor (as did the Corcoran.) Said one member of various boards, "Mrs. Shouse is a very brilliant and determined woman. She snapped up Mrs. Warner right away." For financial support -- either raised from the community or donated personally -- board members are indispensable for most museums, theaters, musical and dance groups. Consequently they are often approached with the careful strategy of courtship. Sometimes the ritual is lengthy and complex. Sometimes not: Some boards are so prestigious and prospective members so eager to join -- out of love of the art or the prestige -- that a simple question is all that's necessary. But most institutions have certain rules for the board game.

The first approach is usually limited to a casual chat. "You usually find it more graceful to do it in person -- at a party or a luncheon or even another board meeting," says Curtis Winsor Jr., 41, a businessman who was recruited for the board of the Corcoran by David Lloyd Kreeger, one of the most ubiquitous and successful board members in town. Winsor also serves on the Arena Stage board.

Generally the contact is made after the prospective target's special interests are known. (Armand Hammer, for example, is thought to have little interest in theater, so there's generally no point in even trying to get him for a theater board.)

I always get a hint that I'm going to be asked to join something," said one socially prominent woman. "Someone will say to me at a party, 'Oh, I know someone's going to ask you to do something very important.'"

That first phone call -- and who makes it -- is very important," says one board member. "It should generally be someone that the person knows and respects."

It can take a while. The Children's Museum called fund-raiser Esther Coppersmith for a couple of months before she finally consented -- but only to lunch. (She's now on the board.)

Sometimes it's easy: Hammer says he liked the Corcoran and answered yes on the spot to board president Kreeger. Others remember a protracted courtship -- including an elegant, pull out-all-the-stops dinner at the F Street Club with other board members before he joined. As soon as Hammer joined the museum in 1977, everyone else in town wanted him.

Sometimes it won't work at all. "once you fund-raise for one group, everyone wants you," says celebrated fund-raiser Scooter Miller. "I get all sorts of calls. Every theater calls and wants to have lunch. Pretty soon, you're spending all your time having lunch and telling people how to raise money. I know they shouldn't be spending their money on me. I usually am pretty honest with them. I don't want to go on a board if I don't have time to really work."

The lunch/dinner appointment is always tasteful, low key. "David Lloyd Kreeger is very good at this," says Winsor. "When he wants people, he takes them to lunch at the Metropolitan Club. When he's really interested in someone, he has them over for dinner. When you've had dinner seated in a dining room surrounded by 14 Monets, it's very hard to say no."

That's how Winsor was approached by Kreeger for the symphony board. "It was only financial matters that prevented me from joining. I was just spread too thin over other boards."

Miller was approached by Kreeger and Mandell Ourisman, two board members of the NSO, about taking on the fund drive. They took her to Sans Souci. Later, when Miller had accepted the job and wanted Vincent Burke, chairman of the board of Riggs Bank, to work with her on the drive, she, Kreeger and Ourisman took him to San Souci. (He later accepted.).

Some restaurants have seats so close people can hear everything you're saying," says Miller.She prefers: The Palm ("they have booths"), Le Pavillon, Maison Blanche, La Bagatelle.

When Austin Kiplinger was approached a few years ago about heading the NSO fund drive, Kreeger and Miller took him to the Cosmos Club for lunch "Those two are a persuasive pair," said Kiplinger, laughing. "They threw the blocks to me. They talked about the need and my interest (in music) and the obligation to do something for the thing I loved. I thought I said, "I'll think about it." I found out later they thought 'd said, 'yes.' "In 1976, he became chairman of the drive and in 1977 joined the board.

"You stress the positive side," says Kiplinger. "I'm very straightforward, I say to someone, 'Here are the demands of the job and here's how you could handle it. But we need you personally during some things.' That way, they don't feel mousetrapped later."

But many do. Once they join a board, members discover the hard facts of the job, and fund-raising is foremost. It can be agravating.

It isn't much fun to be sitting there with a price tag on your head," said the spouse of a former National Symphony board member. "The symphony is No. 1 on money. It got to be such a pain. Every time my husband turned around, he was getting a phone call at 9 in the morning -- 'We only need $500 to put us over the top.'"

However, most boards have fairly straightforward guidelines about how much each member is expected to raise or to donate:

For the Corcoran board: $5,000 annually. The symphony: $5,000 in years past; this year, when the symphony is in serious financial trouble, $10,000. ("we have some very wealthy people on our board," said former NSO board president David Lloyd Kreeger. "but you have to adjust that figure. Some can't even afford $5,000.")

The Capital Children's Museum: $2,500. Arena Stage: $2,500. New Playwrights Theatre: $1,000 (not including subscriptions and benefit tickets board members are expected to buy.) Washington Ballet: $500 to $1,000. Washington Project for the Arts: $2,500.

In recruiting board members, money is important. But money alone is often not enough.

When I hear people discuss who would be good to be on boards, there's always on premise," says Peggy Cooper, one of the founders and board members of Workshops for Careers in the Arts. "Who's rich, and who knows rich people? That premise is wrong. First, there aren't that many rich people in town and they all know each other.Second, rich people have as many airheads as any other group. If you choose only on that premise you end up with too many airheads on your board."

That's why boards also seek out members with proven fund-raising abilities, good contacts and valuable skills like law and accounting which can be donated to the institution.

A business on the board of a small arts organiation can both do the books and give the organization "a seriousness of purpose," according to Pat Matthews, a vice-president of the board of the Cultural Alliance.

But according to most Washington arts administrators, there just aren't enough business executives to go around. And some black executives are on so many boards that working on them could be a full-time job.

I think there's a lot of vying for the Time Inc. people," said one observer. "and they'll fight over the bodies of the Mobil people when they get here."

But having the time to help can be as valuable as business skills Several years ago, Elaine Silverstein -- wife of tax lawyer Leonard Silverstein, who last week was elected chairman of the NSO board -- accepted the job of chairman of that white-tie benefit extravaganza known as the National Symphony Ball. She says she spent a whole year planning it and hired, on her own, a personal secretary. Afterward, the NSO put her on the board.

And there is no substitute for the cachet of a famous name. One very prominent Washingtonian attended practically none of the meetings of a board he sits on. In fact, when he was mailed a ballot to vote on new members, he had his secretary call the organization and inform them that he couldn't vote because he didn't know the candidates. The organization director's secretary rather testily replied to the board member's secretary: "Perhaps if Mr. ----------- came to some meetings, he'd know what they were voting on."

But the director of the organization has no intention of throuwing the absentee member off the board. "Names are key," she says. "When you're working with funding sources, the first thing they ask for is a list of the board of directors. You can't just have grass-roots people. You have to have some prominent people."

Obviously, the foregoing qualifications are rare, and membership on more than one board is very common in town. David Lloyd Kreeger, founder of GEICO insurance, is a prime example. "I'm on seven or eight cultural boards -- maybe l0," he says. "I haven't counted them up recently." He is currently president of both the Corcoran board and the Washington Opera board.

The NSO board is one of the most generous in the country, according to Kreeger. Out of a total $1.7 million that the symophony needs this year, 20 percent will come from the board -- through direct contributions of fund-raising -- Kreeger estimates. The Corcoran board is responsible for about $250,000 annually.

Art museum boards have special wants. They need money, but they also need collectors. "They're versed in the arts, they have good taste in art, they're knowledgeable thou art," says Kreeger. "There's always the possibility they will contribute some of their art to the museum. They also know other collectors. And some collectors tend to be financially secure. Collectors are excellent for boards."

The Corcoran has several collectors on board besides Kreeger. There's Gilbert Kinney, a former career foreign service officer and once the American counsel in East Java. His collection includes 20th-century European and American art and some Asian art. After being recruited by another board member, Kinney has given the Corcoran a Gilbert Stuart that he inherited and a set of James Rosenquist prints. "You run out of space on your walls," Kinney says. He in turn asked business executive Michael Rea, another collector to join the board of the Corcoran. Another local collector sought after by the Corcoran and others is local businessman Robert Kogod, who owns a modern American art collection.

Nowhere is the advantage of a sucessful board game more apparent than at Washington Project for the Arts.

WPA needed a little bit of everything when director Al Nodal revamped his board. WPA now has an expert at fund-raising [Carolyn Peachey], a lawyer from the staff of the Senate Banking Committee [Tommy Brooks], an architect [James Rich, who heads up their relocation committee], a D.C. councilman [John Wilson -- who helped them through the city government bureaucracy when they were putting up the famous outdoor cowboy boots], and an accountant [Phillip Jacobi from the Arthur Anderson firm -- "They developed a specialized accounting system for us that would probably have cost $8,000," said Nodal.]

They also have a well-known artist, Gene Davis, who contributed 60 prints for a "Friends Drive." (Become a friend of WPA and get a print for $250)

I really wanted to get a board that could have some authority over WPA," says Nodal. "I feel good about it I would never put people on the board for money -- I want people who can work and who are good people. I feel like I've got the best board in town. I just wouldn't work for a board of l0 little old ladies who didn't know what was going on."

The president is Mary Swift, long involved in arts activities. "We felt she was good and could give the nicest parties, " says Nodal.

WPA also has Hirshhorn curator Howard Fox and the noted curator Walter Hopps. "I think our board's really prestigious," said Nodal. "A lot of people would really die to be in a meeting with Walter. He's a myth."

Apparently, the image of the WPA board is acquiring an adequate luster. Nodal says a man recently approached him and said he would make a huge contribution if WPA would put him on its board.

"We're considering it," says Nodal.