Heidi and Bill are one of those polished professional couples who seem to have everything. They have flourishing careers, a close marriage of 4 1/2 years and an elegant town house decorated in splashes of turquoise and black.

What they do not have, however, is what they want most: a baby.

Doctors have told the suburban Maryland couple that they will probably never produce a child. Adoption agencies have told them that no names are being added to waiting lists for infants. And so, Heidi and Bill have joined a small but aggressive group of would-be parents who are trying a direct adoption appeal to expectant mothers -- through colleges and universities.

"By going through colleges," said Bill, 31, a store manager, "we thought we would guarantee one important characteristic: that the mother was intelligent and had a certain perseverance."

Most of the couples are looking to the classified ads section of college newspapers. While such advertisements commonly have appeared in newspapers in cities and towns for the past few years -- The Washington Post, for example, accepts such advertising -- placement in student publications is a relatively recent development.

The advertising, although legal in most states, is controversial. Opponents say couples using the tactic often get babies that would have gone to other couples who have been on agency waiting lists for years. They also say it smacks of baby-buying, a practice that is illegal in most states.

But increasingly, couples who desperately want a child and have despaired of getting one through an agency are running ads in a variety of student newspapers, touting themselves as happily married, loving and responsible people who could give a baby a fine home. The ads do not offer to pay for the baby, but they note that the couple will pick up the mother's medical and legal expenses.

At the University of Pennsylvania, for example, the Daily Pennsylvanian uses the heading "Adoptions" to accommodate the two or three ads it runs daily from searching couples.

In recent editions of the Diamondback, the University of Maryland newspaper, Heidi and Bill's classified ad announcing their desire for "a healthy white baby" ran along with a similar ad by another Maryland couple.

At Cornell, the University of Pittsburgh and Kansas State University at Manhattan, couples have placed ads appealing to pregnant women and then waited for their telephones to ring -- with unknown success. Other student papers recently have been approached for the first time about such ads. Some decided to accept; some did not. The Daily Texan at the University of Texas and the Daily Cavalier at the University of Virginia, for example, have refused to take the ads, calling them improper for a student publication.

On Friday, a woman called the Hoya office at Georgetown University and asked if the newspaper would print adoption ads, the first such inquiry the paper had received.

"It struck us all as very strange," said Tarek Khlat, advertising manager. "We had never had that kind of question before. We're not allowed to run ads for abortions and things like that, so we had to consult the greater powers-that-be: the editor-in-chief, the adminstration. Finally, I called the woman back and told her we would run her ad if she sent the money."

Couples have tried variations on the approach.

In the past few weeks, three couples have sent letters, complete with color snapshots, to the University of Maryland's student health services, asking for help in making contact with pregnant women. "In three years, I had never run across such a thing," said Pat Preston, director of social services. She said she has no choice but to ignore the letters because it is not her job to act as an adoption agent.

The tactics reflect the limited number of newborns available for adoption and the unusual approach some couples are willing to take to get the child they want.

Two million American couples are looking for babies to adopt -- primarily healthy Caucasian babies, according to the National Committee for Adoption.

Roughly half of the couples go the agency route; the other half opt for what is called private adoption and use ads, fliers, adoption networks and word-of-mouth to find a woman who is pregnant.

All are in a competitive situation. Only 50,000 infants are available for adoption each year, according to the national adoption committee.

Adoption officials attribute the baby shortage to societal changes: the reduced stigma of unwed motherhood that has led more single women to keep their babies, the availability of birth control and, since 1972, the legalization of abortion.

"Getting a white infant is almost impossible," said Sharon Benjamin of the North American Council for Adoptable Children. "The wait can be nine or 10 years."

Most agencies these days are not even adding names to their waiting lists for infants. The Barker Foundation, generally recognized as the largest adoption agency in the Washington area, last opened its waiting lists to new applicants in June 1983. At this time, 300 couples are waiting just to get on the waiting list, said foundation spokeswoman Julie Emmons, who declined to say how many applicants already are on the list.

While special children -- those who are older, those who have mental or physical handicaps and those who must be adopted in sibling groups -- are readily available, the child of choice is the healthy white infant, adoption officials agree.

"We admit we're selfish," said Heidi, 30, an interior designer who has had two miscarriages. "We want to have a family."

"We want what's called a blue-ribbon baby," Bill said. "We're not out to save the world."

Discouraged by adoption agencies, yet impatient to become parents, the couple decided to launch an independent campaign for private adoption a year ago.

Unlike in most agency adoptions, the mother in a private adoption might meet with interested couples and choose her baby's prospective parents. In most states, couples generally are allowed to pay legal costs and medical expenses connected with the pregnancy and birth but may not pay for the mother's clothing or other living expenses or make a flat payment for the baby.

Generally, however, a private adoption must follow the same procedures as an agency adoption. Under Maryland law, for example, the prospective parents have to participate in a home study by a licensed social worker. The baby's mother and the father, if located, have to sign away their rights to the child. And the adoption must be finalized before a judge.

Sometimes the mother is able to maintain contact with the adoptive parents, sometimes not. Heidi and Bill, for example, have arranged a post office box and installed a special phone line to carry out their search, thus ensuring privacy.

"I'm sorry," Bill said, "but once we adopt, it would be our baby."

In addition to the University of Maryland ads, the couple has sent letters to social service agencies across the country that begin: "We are a close couple looking to share that closeness . . . . " They also have placed ads in small-town newspapers such as the Frederick Post.

So far, they have had no response.

A New Brunswick, N.J., couple, also in their 30s and hoping to find a baby, are in a similar situation. Their ads are running in the Daily Pennsylvanian and in small newspapers in rural Pennsylvania and Arkansas.

"We went to see an attorney," the woman, who asked not to be identified, said in a telephone interview, "and he gave us a list of newspapers to put our ads in. He told us that within six months to a year, we should have our baby."

Attorneys who handle private adoptions in Washington, Baltimore, New York City and other large cities are advising their clients to advertise, a development that angers some.

"We would like to see such advertising outlawed," said William Pierce, president of the National Committee for Adoption. "We consider it pandering. What you have is naive young women with a commodity desperately sought by sophisticated couples with sophisticated legal knowledge."

"I sympathize with the couples," Pierce said, "and I understand their desperation, but these ads amount to practicing social work without a license."

In such a competitive market, however, couples such as Heidi and Bill believe that no option should go unexplored.

"The only thing we can hope for," Heidi said, "is that there is a birth mother out there who will meet with us and want us to take her baby.

"My expectations always were that when I was 30, I would have a station wagon, a dog and two kids," she said. "Well, I have the station wagon. I don't want a dog. And I do want the kids. I believe we have a lot to offer."