First, they're alive. About a fifth of children abducted by non-family members are killed, and most of them are dead within three hours of being snatched. It could be worse and thank heaven it's not.
Second, they've either been rescued or managed to escape. Someone's been a hero, or the abductee has despite their experiences retained enough vim and awareness to get out - hooray!
Thirdly of course there's a grieving family somewhere which will experience an elation and joy it's hard to put into words. Someone they love has almost back from the dead - let the cheers resound.
But the sight and sound of crowds cheering the news that three missing girls - Amanda Berry, Gina DeJesus and Michelle Knight - have been found alive after up to 13 years in captivity in a Cleveland basement misses the point that there's an awful lot more to worry about than celebrate.
The cheering reduces their story to the end of a feel-good movie - to a bedraggled Bruce Willis kissing his wife at the end of Die Hard, or Bill Murray standing on a New York cab after the Ghostbusters save the city from a giant marshmallow man.
It's not a movie. It's real-life. Children snatched from the street in real-life and locked in a cellar and being raped and having children of their own and, more often than not, having to rescue themselves because no-one else does.
Not so feel-good when you look at it like that, is it?
Amanda was taken at the age of 16, in 2003. Gina disappeared at the age of 14 in 2004 and Michelle was a little older at 20 when she vanished in 2000. They were the centre of a massive publicity campaign by their families, their names and pictures were widely-known, the police investigated, yet they weren't found until Amanda managed to scream out of a locked door and a neighbour happened to hear her.
At first the police didn't believe it was her, and she had to beg them to free her fellow prisoners before their captor returned. Amanda's got a six-year-old daughter with her, and there were other children found in the house too.
How does any of that happen? How can a young woman disappear off the street and never be seen again? How does a homeowner buy loads of heavy chain, fit it to rings in his ceiling and have three adults and a bunch of children living in his house and no-one notices? How did the police not know there was a lunatic in that street? How does anyone think they could get away with it?
More important than all of that, how many more are there?
Natascha Kampusch was abducted at the age of 10 and held for eight years in a specially-built cellar. Elizabeth Fritzl was thrown into the family cellar at the age of 18 and held for 24 years by her own father. Jaycee Lee Dugard was snatched at the age of 11 and kept for 18 years in the back yard of a known sex offender. Elizabeth Smart was taken from her own bedroom at the age of 14 and held for nine months. Katie Beers, at the age of nine, was thrown into an underground bunker by her stepfather and held unnoticed by her school or social workers until he handed himself in.
With the Cleveland news, that's six big incidents of children being abducted and held captive. They weren't held halfway up a mountain - they were all in the suburbs, surrounded by neighbours. They didn't disappear unnoticed - they all had at least one parent who cared. And in most cases the authorities had some contact with the men responsible, and they didn't spot it either.
There didn't use to be children found chained up in cellars. When the Kampusch news broke I remember thinking 'wow, eight YEARS?' and wondering if, now one person had done it, other depraved perverts would copy him.
Elisabeth Fritzl got out just two years later, had been held far longer, had given birth to seven children half of whom lived in 'the real world', and this had happened in the same country. Two cellars of children in Austria? What is that nation up to?
But then I remembered years earlier Belgian paedophile Marc Dutroux was found to have kidnapped and held four children in his house. Two of them starved to death in his cellar, while the police investigated him for car crimes and his wife happily fed her pet dogs. Maybe it was just a European pervert fad.
Then Jacey was found, and others who'd been found and released more quietly began to speak up. With the release of Amanda, Gina and Michelle the wealthiest nation on Earth has had at least four high-profile cases of children being locked up alive and it looks more like this might be a phenomenon which could, just as easily, be in our own street.
Two in Austria, four in America, one in Belgium. How many in France? What about Germany, Spain, Russia, Britain?
Most missing children are just that. They wander off, run away, or get lost, and the vast majority of cases are solved in a few hours. Some are abducted but most abductions involve family members or someone who's known to them, and parents usually know who's got them.
Then there are a tiny few cases, most famously like that of Madeleine McCann, where a child simply vanishes. There are few witnesses, no suspects, and most obviously no body.
In the UK half of all child abductions are by strangers, most are failed attempts, and nine per cent are successful. In between the sex assaults, murders and escapes, what do you think the chances are that there's at least one basement involved?
And why don't we know where it is? Most of the children we know have been held in captivity are female, and most involve sexual assault. A rapist doesn't one day just snatch a child off the street and throw them in the cellar - they've worked their way up to it, and more often than not are experienced at bullying, coercion and control.
Josef Fritzl had a previous conviction for rape and had abused his daughter since she was 11. He locked his own mother in the attic, and his wife lived in fear of him. Yet for quarter of a century he didn't raise an eyebrow among his neighbours or the authorities.
Perhaps this is a phenomenon of the western world. Perhaps those that want to rape know they'll be prosecuted if they let their victims go, and caught by forensics if they kill. Perhaps modern, middle-class life means the neighbours don't stick their noses in, and overworked schools and social workers find it easier to believe a lie than think the worst of a parent. Maybe, somehow, the fact we're all so busy doing our own thing makes it easier for awful people to do theirs.
It was only a few decades ago that people pretty much knew everything about the other people in their street. Their children played together, everyone went to the same pub, worked at the same place. If just one tiny thing changed you knew about it - someone shifting half a ton of heavy chain indoors would need to explain it. People took note rather than thinking it was polite to ignore things, like the cast of The 'Burbs telling themselves their new neighbours can't possibly be mass murderers.
It's obvious when you think about it that being better at catching bad guys would force them to evolve a new trick to evade the law. And even though people like Fritzl get caught in the end, it's a bit late when he's had his fun for 24 years. He's locked up in much better conditions than either his mother or his daughter enjoyed, and the only bonus is that his victims know they're finally safe.
But had they been safer sooner, Elisabeth Fritzl might not have to live in a house where she has had all the internal doors removed. Her children might not have to come to terms with the fact they were born of rape, although the latest reports show they're amazingly well-adjusted.
The stories of the women those snatched children grew into show the years after captivity are more than just difficult. Elisabeth takes up to ten showers a day, because she could never get clean in the cellar. Natascha Kampusch is said to regularly visit the house where she was held, and the three women freed in Cleveland will all react differently to both their abuse and release.
Maybe the only way we can do anything about what seems to be a new trait among bad people is to take more note of them in the first place.
Unfortunately, we live in a society where domestic violence isn't taken seriously, where courts find excuses for people accused of rape when there are none available to their victims, and where known instances of police, the NHS, the state broadcaster, prison service, government and even a Prime Minister all found to be consorting with, aiding and even unknowingly abetting child abuse is not given the national inquiry it surely demands.
Humans can be a bad bunch, and the only thing which stops some people being appalling is knowing they'll be found out. Yet if we do not make an effort to stop the abuse, rape, and control when it first rears its ugly head we cannot hope to stop it building to the point where someone decides their logical next step is stealing a child and hiding them in the cellar.
Not having found anyone in such a horrible situation used to mean that it couldn't possibly be happening, but more and more it occurs to me it just means we haven't found them yet. The cellar probably is there, if only we could bear to look for it and stick our noses into things we'd rather not see.
When you've found a freshly-built cellar and stopped someone being locked in it - that's the right time to cheer.
Be glad they're safe, but be mad they weren't safer.