NEW YORK (AP) -- When Jerry Damman first got news his son may have been found after vanishing from Long Island more than 50 years ago, he said it ''was almost too good to believe.''
It turned out he was right.
His new hope was dashed when DNA tests last week revealed that John Barnes, the man who claimed he was the missing boy, actually wasn't -- an outcome that didn't surprise law enforcement officials and experts.
They say a storybook ending was a long shot from the start. Past cases show that it's rare for someone purporting to be a long-lost child to suddenly come forward, and rarer still that he or she ultimately proves to be the person who vanished.
''That would be extraordinary,'' said Joseph A. Pollini, a former New York Police Department cold-case investigator now teaching at John Jay College of Criminal Justice in New York.
At least 15 people have approached the National Center for Missing & Exploited Children in the last decade with beliefs like Barnes', but none turned out to be the missing children they sincerely thought they were, said Jerry Nance, who oversees long-term missing child investigations for the organization.
Like Barnes, most started with a feeling that they simply didn't belong in their families, then researched old missing-child cases and found one that seemed to fit, Nance said.
More than 778,000 people nationwide were reported missing last year. Nearly 80 percent of them were under 18, FBI statistics show.
Most missing children are found fairly quickly, according to a 2002 study done for the federal Department of Justice. The study found fewer than 10 percent of missing children were kidnapped, usually by relatives.
Police in New York -- where 8,202 missing persons cases were opened last year -- also say that nearly all children reported missing soon turn up.
One exception was the headline-grabbing case of 6-year-old Etan Patz, who vanished 30 years ago after leaving his apartment to catch a bus to school. The disappearance remains unsolved, though the family members have said they believe a baby sitters' boyfriend, a convicted child molester, killed the boy.
The boyfriend, who remains in prison, has not been charged in the case. But he was ruled responsible for the boy's disappearance in a civil case. A judge ordered him in 2005 to pay Etan's family $2 million.
New York City police procedures require an immediate and aggressive search for missing children under 16. Detectives can call in police helicopters or boats, and they often contact social workers because many disappearances involve child custody disputes.
In the Long Island case, Stephen Damman was 2 when he disappeared while his mother shopped on Oct. 31, 1955.
Investigators chased down leads around the country, to no avail. A hope for a major break came and went in 1957, when a boy's body was found buried in a cardboard box in Philadelphia. But it was determined not to be Stephen's.
Other police departments have contacted Nassau County investigators about four times in the last six years about cases that might match Stephen's disappearance, but none of the inquiries led anywhere, Nassau police Lt. Kevin Smith said.
Detectives were initially leery when Barnes, an unemployed Michigan laborer in his 50s, contacted them earlier this year, Smith said. But when Barnes called back some weeks later to say a private DNA test had shown he and Stephen's sister might be related, Nassau police turned the case over to the FBI.
The FBI said Thursday that more extensive DNA tests found Barnes and the woman could not be siblings.
While the finding may send the Damman case back into limbo, it isn't the only 1950s missing-child mystery getting renewed attention.
As Barnes' claims made headlines this week, FBI agents and local authorities explored possible leads in the disappearance of Daniel Barter, who vanished on a family camping trip along Perdido Bay in southern Alabama on June 18, 1959, when he was 4 1/2 years old.
Hundreds of volunteers conducted a manhunt and even gutted alligators to see if they had eaten the boy. Then-FBI Director J. Edgar Hoover sent the family a telegram pledging the agency's aid.
But the investigation stalled before new details emerged in recent years. A conversation about the case was overheard in a doctor's office, and investigators got a tip that someone elsewhere was familiar with an abduction in the area in the 1950s, FBI Special Agent Angela Tobon said.
After five decades, Mike Barter isn't sure what he thinks happened to his older brother. But he, his siblings and supporters held a candlelight vigil Saturday at the campsite in Lillian, Ala., to draw attention to the case's 50th anniversary.
''The more you bring any missing person up,'' he said, the more chance ''some little something -- some wording, something to flash back in someone's memory -- brings back something that they can work with.''