A world-weary, big-city private eye joins forces with his daughter, an attractive redhead who spent her youth wishing dad would quite the trouble business. It could be the plot for a television series, but for Phil and Billie Davision of Washington, D.C., it's real life.

Six months ago Billie, 23, received a private detective license and her father's blessing to join him on the mean streets, tracking down cheating spouses, serving summonses to reluctant litigants. Her gender and appearance have given her an advantage over older, mostly male detectives who have difficulty blending into backgrounds - detectives who look the role - like Phil Davison.

"After 28 years," he says, "you begin to unconsciously resemble the private detective I'd rather not look like."

On the other hand, says Billie: "If you think you're being followed by a private detective and you're looking over your shoulder, you're going to look right past me." She has put on jeans, piled her hair in a bun, borrowed a friend's dog and walked around the grounds of private schools unnoticed. Recently she approached someone who had for six months avoided service of a subpoena in an insurance case; she got her man as he walked leisurely down his neighborhood street. "Women don't constitute trouble to a lot of people," she says.

Unlike most private eyes, Phil Davison does not advertise, working mainly on referrals from lawyers. He is known as a conscientious man in a field crowded with charlatans. He refuses to break the law by bugging - he says he's allergic to striped sunshine" - and he's defensive about divorce cases, which are the bulk of his work.

Once, after an associate told him of solving a jewel robbery, Davison thought about his work, the long nights parked outside apartment waiting for a tryst to end.

"It struck me my friend had only been talking about money," Davision says. "And I was about to gather evidence which might have a profound effect on whether a small boy would be leaving his green backyard to live with the other parent in a rooming house. I realized that boy's future, and the future of possibly five or six other persons, would be affected by my work, which was more important than mere dollars and cents."

The Davisons generally work alone, at a rate of $25 an hour. Billie calls her father "Ace" or "Chief" or "O.M." (for "Old Man") and she says they are more like roommates than father and daughter. Phil says it's nice not having to worry about the veracity of his partner: "When it's red out there on the streets, she's not going to report it pink." And for the first time in years, he has taken a week's vacation, leaving the store in Billie's hands. In return, he tries to give her some evenings off to spend with the Navy officer Billie dates. It's a living, and as Phil Davison says, retirement is a dirty word.