My first phone call went to a Jordanian who likes Iraq and has many Iraqi friends. "Nothing to it," he said after making a round of check calls."I can't be 100 per cent sure, but I don't believe it."
It is possible this source might deny the story in the interests of President Saddam, so the second call went to a Jordanian with excellent contacts within the Jordanian and Iraqi security apparatus, but no friend himself of President Saddam's regime.
"It all smells to me," he said. "Uday has enough enemies to claim this is true, and there's enough bullshit flying around Amman for you to believe anything. But I'll tell you this. The oil markets are very interested. If people believe Uday was shot in Baghdad, people will believe the Iraqi regime is crumbling, that Saddam is about to fall and that sanctions will end. So there could be lots more oil on the market and the price of oil will move in the way an oil speculator will want it to move - down."
Now it is true that the government medical centre in Amman has treated members of President Saddam's family before. But in Baghdad, Western reporters saw Uday on state television three nights ago, greeting an official delegation in the capital. That same day, Uday's picture appeared in the Baghdad press, apparently attending a sports event in northern Iraq.
Convincing proof then that the young and much-beloved son - who shot dead his own bodyguard in a bar-room brawl almost a decade ago and said in 1990 that the executed Observer journalist, Farzad Bazoft, deserved to be hanged "a thousand times''- is still alive? Perhaps, but the film and the picture might not be contemporary.
So a third call to an Iraqi citizen visiting Cairo - where the story first emerged more than a week ago and was swiftly picked up by the Kuwaiti press. "There's obviously no way of knowing," he said. "But I immediately doubted the report. I can't believe that Uday would be taken to Amman. There are plenty of good surgeons in Baghdad. And though there are precious few medicines available to ordinary Iraqis under Saddam's regime, this definitely does not apply to the president's family."
Then came denials from Jordan and some very heavy doubt in stories from two of the key international news agencies with correspondents in Jordan. Most of us, after all, could paper our bathroom walls with Iraqi coup reports that turned out to be wishful thinking on the part of Western governments.
A final call, then, to a UN source who should be aware of any flights out of Baghdad, where the UN's monitors know of helicopter or fixed-wing flights - authorised or otherwise - leaving the country. "We know nothing about it," said the source.
Note the anonymity of all involved. President Saddam may be corralled in Baghdad, but the long arm of the Iraqi Baath party casts a serious shadow over anyone who chooses to speculate in public over the health of Saddam's heir apparent.
Woe betide Middle East hands who pooh-pooh the biggest story out of Baghdad since the Mother-of-all-Battles that wasn't. But on all the evidence, it looked last night as if Uday will live to kill another day.