District parents yesterday gained slightly more flexibility in giving their children surnames after the D.C. Council made a third change in three weeks to the city's laws governing the matter.

Under the latest version, parents can give their children any surname that has a connection to either the mother's or father's names or the names of their ancestors.

The amendment was offered yesterday by council member Kathy Patterson (D-Ward 3) and adopted without debate.

Council members said the matter will finally be put to rest. The issue of surnames has been debated by council members and residents since spring, when an Arlington couple whose son was born at Sibley Memorial Hospital in the District sued the city after discovering that a directive required married couples to give their children the father's surname.

That directive was issued by the Department of Health in May 2000. Some people argued that the order was a violation of women's constitutional rights. In May, the city government issued an emergency resolution, effective for 120 days, that allowed married couples to use the mother's surname.

Last month, the council voted 7 to 6 to allow parents the freedom to give their children any surname. But the council later reversed its position when David A. Catania (R-At Large) changed his vote. Opponents of the liberal version of the law argued it might lead to instances of fraud or give parents the opportunity to abandon their children. The council then voted 7 to 6 to require parents to give their children either the mother's or father's surname or a hyphenated combination of both.

But Patterson argued that version was still too restrictive to survive a court challenge. Her amendment allows parents to give their children a completely new surname provided that it is derived by combining the parents' two surnames. Parents also may give their children a completely separate surname provided the parents sign an affidavit swearing that the name has a family connection.

"I think this meets most of the concerns of the folks who shared their concerns," Patterson said yesterday. "This is broad enough to give parents pretty good flexibility."

Patterson had worked to make the law more liberal after hearing from Addy Schmidt, an American University graduate student who, along with her husband, had been barred from giving their daughter Emma a combination surname derived from her and her husband's last names.

Schmidt supports giving parents complete freedom to choose a surname, but she said she was pleased with yesterday's compromise.

"We're thrilled," said Schmidt, who ended up giving Emma her last name and now will go to court to change Emma's name to the combination surname. "We've been working on this for 18 months."

After all the machinations, Catania said, "It's done. This won't come back up for some time."