Three years ago, Brigham Young University decided that the time had come to inventory its sprawling art collection, a large mix of paintings and drawings scattered around the campus. There was no formal museum, so art department officials found themselves unlocking closets and forgotten storage rooms, trying to match their paper records against the objects they found.

Their records, by all accounts, were not very good, but the officials quickly came to the conclusion they had feared: The collection had been looted. There had been few safeguards in the preceding years and BYU was paying the price. In all, about 1,200 pieces of art were missing, almost 10 percent of the university's holdings.The missing pieces ranged widely from student paintings that had little or no value to works by highly regarded artists such as French Impressionist Claude Monet and the American painter Winslow Homer. Eventually the university calculated its monetary loss at about $4 million.

Just as costly were the wounds to the university's pride and the loss of part of its cultural heritage - a large number of missing paintings were by Mohonri M. Young, grandson of Mormon pioneer Brigham Young.

And worst of all, it looked like an inside job.

In similar circumstances, many other institutions would have kept quiet about the losses, fearing that publicity would discourage future donations of art. BYU decided to do just the opposite.

Not only did university officials announce their findings, they embarked on a campaign to get the art back. With missionary zeal, the university launched a detective search for painting after painting, tracking their movement through a maze of dealers and owners.

"There are dozens of other universities and museums that have suffered losses like ours. It's just that you don't hear about them," said Virgie Day, the manager of the fine arts collection at BYU. "This is a crime that almost always gets swept under the rug because people who run the institutions don't want to be embarrassed."

Most art experts would agree with Day. As the value of the artworks has skyrocketed over he past decade, institutional collections that are not carefully managed have increasingly become the target of crooked dealers and thieves.

Constance Lowenthal, executive director of the International Foundation for Art Research in New York, said it is impossible to estimate how much thievery takes place because most institutions are successful in covering it up. But the problem is serious and growing, she said.

"Most often you see this happen at institutions that never set out to establish an art collection in the first place," Lowenthal said. "It just sort of accumulates through donations. The institution doesn't realize how valuable the stuff has become and there's no professional care-taking. Eventually someone spots this vulnerability and they make off with the art."

In the case of BYU, the search for the missing art has left investigators knocking on some interesting doors. Two drawings missing from the university collection eventually wound up in the hands of noted collector Armand Hammer. Another painting currently resides at the Metropolitan Museum of Art in New York. Still another was located in the possession of Baron Hans Heinrich Thyssen-Bornemisza, a Swiss industrialist whose collection is widely regarded as one of the finest in the world.

BYU hastened to add that none of these collectors took part in the looting of the BYU holdings or even had knowledge of it. All of them are what is known in the argot of art theft as "innocent buyers," meaning they acquired the art after it had changed hands several times and had no reason to believe it was tainted.

Unfortunately for BYU, some of the thefts occurred in the late 1960s, yet the university did not track them down until the late 1980s. BYU's missing artworks often were shown publicly without the university intervening. These legal barriers may be one reason why the university's campaign has not met with much success.

Thus far only about 40 of the 1,200 missing pieces have been recovered, and art department officials say they expect that the great majority of artworks will never return.

Chief among the resisting owners is the Metropolitan Museum of Art, which has refused thus far to return a painting by American artist J. Alden Weir. Ashton Hawkins, counsel for the museum, said it has resisted primarily because the museum believes that BYU abandoned its claim to the painting by waiting so long to announce its ownership.

"I doubt very much that they have any legal claim," Hawkins said. Negotiations are still under way.

With the legal situation so murky, BYU has decided to make an ethical appeal to current holders. Last year the university published a list of the more important missing works in IFAR Reports, a New York journal specializing in stolen art, and asked for information as to their whereabouts. And soon, the university will mail a letter to the known holders asking for their cooperation.

"Lawsuits are very expensive and we don't know that we would prevail," said William Fillmore, associate general counsel for the university. "For the most part we are going to have to rely on people's good will and sense of what is right." Just how BYU got into this fix is a sad story. It began in 1960 when the university was bequeathed the art collection of Mohonri Young, an artist himself and a member of one of Mormondom's main families. The Young collection doubled the size of the university's holdings overnight, and added paintings by Weir, Homer, Maynard Dixon and even some drawings by Rembrandt.

Without a museum, the art was made available to faculty members who needed wall decorations. Professors would be allowed into the storage rooms, where they could choose from among the paintings, some of which were worth tens of thousands of dollars.

One member of the art faculty who realized the importance of the collection was Wesley M. Burnside. An expert on Western American painting, Burnside was driven by the desire to build an outstanding art collection at BYU and a grand museum.

The artworks were important to Burnside not because they represented the art he craved for the university but because they gave him pieces that he could trade.

Working with a coterie of art dealers from New York, Los Angeles and Salt Lake City, Burnside soon was making deals at a feverish pace. Some of the trades were approved by a faculty committee appointed to oversee the collection, but, according to BYU officials, many were unauthorized trades made by Burnside alone.

Alas, Burnside was not very good at the trade game. Dealers walked in with junk and walked out with treasures, BYU officials now contend. In some cases, they said, Burnside would cement his deals by throwing in "sweeteners," or extra works from the storage room. Few if any records were kept of the deals.

"I would say Wes lost hundreds of thousands in his investments," said one colleague who asked not to be identified. "The thing is, Wes was trying to make a killing so he could donate all the money to the university for the museum. I believe that. Wes always thought he was on the verge of pulling it off."

Ironically, the disaster remained hidden for years after Burnside retired in 1984. James Mason, a new dean of the art department, heard rumors that paintings from the BYU collection were being offered for sale on the international art market. Curious, he ordered an audit of the collection, and the awful truth was finally revealed.

Eventually, Burnside was convicted on one count of unlawful dealing in university property and fined $500. In one indication that he did not profit handsomely from his misdealing, Burnside asked the court for a delay in paying the fine so he could raise the money.

Frustrated over the results of their campaign to reclaim the art, university officials said they may press more civil suits and criminal actions. Most of those, they said, will be directed at dealers who preyed on Burnside and the university.

Or they may just give up. No institution has ever been so open about a massive art theft, they said, and no institution has ever worked so hard to get it back.