Even when Siamese twins don’t share a single, abnormal heart as Amy and Angela do, they usually share other internal organs–and surgical separation rarely produces two fully functioning individuals. Since the first successful separation in 1689, according to a recent study, fewer than 100 such operations have resulted in the survival of one or both twins. In no-win situations like the Lakebergs’, doctors have an obligation to set clear limits, says Arthur Caplan, director of the Center for Biomedical Ethics at the University of Minnesota. “If something is impossible to do, it is clearly a violation of medical ethics to [try to] do it…regardless of what the patient or the family wants.”

The Lakebergs found out when Reitha was 12 weeks pregnant that she was carrying Siamese, or conjoined, twins. She considered an abortion, but couldn’t go through with it. Although the Lakebergs are Roman Catholic, Reitha says her decision was only “partly” because of her religion. “It’s just the way I felt.” The twins, delivered by Caesarean section three weeks before term, now weigh 12 pounds. Four times a week, Reitha and Ken make the 2 1/2-hour drive from her sister’s trailer home in Wheatfield, Ind., to visit the babies. Because a respirator bypasses the infants’ windpipes, they don’t make normal crying sounds–but Ken and Reitha can still cuddle them. “When I hold them, I fall apart,” says Ken, 26. “This is a nightmare.”

To many doctors and ethicists, surgery that has almost no chance of success is morally and economically indefensible. “It’s certainly not the best way to spend scarce resources,” says Caplan. But the Lakebergs, who have no medical insurance, refuse to let the extraordinary expense of surgery stand in their way. “Families won’t say ‘stop’ because they don’t want to feel guilty,” says Caplan. “You’ve got to present options in way that lets doctors bear the responsibility and the burden.”

Parents like the Lakebergs should be told that the surgery their babies would undergo is a research experiment, not a treatment, says Dr. John La Puma, an ethicist at Chicago’s Lutheran General Hospital. “it shouldn’t be portrayed as being for the babies’ good.” One twin would die instantly, when doctors clamped off her blood supply. The other would need massive reconstruction of the abnormal heart. if that baby survived, it would probably be only for a few painfilled weeks. The humane alternative, doctors at Loyola believe, would be to take the twins off life-support systems and allow them to expire peacefully. It’s hard to see how this story can have a happy ending.