Often, 5-year-old George Jeffries asks his mother Carole how she found him. She tells her adopted son: "Once upon a time a girl named Carole looked for the perfect little boy. She looked and she looked. Finally a fairy godmother named Marie called and said, 'We've got the perfect [son] for you.' "

The real-life account of Carole Jeffries' efforts to adopt a child is no fairy tale. As a lawyer and a single woman, Jeffries repeatedly encountered adoption agencies that frowned on adoptions to single women "despite the publicity surrounding single parents" in favor of the family of "Ma and Pa, a white picket fence, 2.5 kids and a dog."

Jeffries finally came to the sparsely furnished row house office of CARE, the Children's Adoption Resource Exchange, at 1039 Evarts St. NE, where she found a staff that openly recruited nontraditional adoptive parents. Through CARE, Jeffries adopted George 18 months ago.

Today, George "is a different child," said his mother. He had been withdrawn and silent and appeared to be a slow learner when he first came to live with her. Now, she says, he is an extremely affectionate, alert and intuitive youngster whose radiant brown eyes do not miss a thing.

CARE is one of a few Washington area adoption agencies dedicated to finding homes for "special needs" children, whose age, race, mental or physical handicap, or situation in sibling groups makes them hard to place in permanent homes.

Unlike other agencies, which may have policies that filter out single parents, CARE is more flexible, said Roselyn Williams, a caseworker supervisor for adoption services at Lutheran Social Services in Washington.

"The bottom line is finding a kid a home," said CARE director Gloria Swieringa, 47, who has not let her blindness prevent her from having a family. She and her husband have a child of their own and have adopted four.

Two years ago, when CARE was $20,000 in debt and about to go out of business, Swieringa took control of the agency. Adoption fees, often reduced for low-income families, and the small grants that trickled in were not enough.

At the peak of its financial crisis, in November 1982, Swieringa helped rescue CARE with an emergency fund-raising campaign. "I went to the public and pulled in $4,000 in about two weeks," she recalled.

The agency has since crawled out of debt with small grants from foundations, generous contributions from the public and support from the church community through Swieringa's "Touch Somebody's Life Campaign."

On Nov. 12, Swieringa received her first paycheck from CARE. "That's how far we've come," she said proudly.

On a $19,000 budget last year, CARE's staff of Swieringa and six part-time social workers placed 26 children. This year, CARE has found homes for 15 children on a budget of $4,000.

As a noncustodial agency, CARE acts as a kind of matchmaker service between prospective foster parents and adoption agencies. It does not house or take care of children. CARE provides evaluations, called home studies, of prospective families to the adoption agencies, which make the final decision on the adoption of foster children in their custody.

Although CARE is out of debt, its financial status is still precarious, in part because the standard $2,500 adoption fee for prospective parents often is waived.

"There are many black families that would make excellent adoptive families. Would you leave a child in the system because that family can only pay $1,000 or $550?" Swieringa asked.

After graduating from Georgetown University in 1957 with a double major in Russian and French, Swieringa met her husband, George. As a biracial couple, Swieringa said they encountered racism from an unexpected source.

The attitude on the street was "not that bad at all. But we got institutional discrimination from adoption agencies," Swieringa said.

Swieringa became interested in adoption "as soon as I found out I could not continue to bear children. I had one child at that point . . . . We were turned down several times by agencies and were refused a home study. They were not willing to see whether we could parent," she said.

Since the Swieringas adopted their first child, a 7-year-old blind boy, nine years ago, local agencies have learned that they are good parents, despite her blindness.

In fact, one D.C. government agency had heard of the Swieringas and asked if they would be willing to adopt Aaron, a 19-month-old child who had brain damage and weighed only 15 pounds.

Today, he appears healthy and inquisitive as he scampers on and off his mother's lap at the CARE office.

"He was our miracle. He's come a long way from being a nonverbal, moderately retarded child," Swieringa said with a smile.