Strangely enough, the 'best' way to hang someone comes up in the history of mathematics.
It is generally recognised that the first ever example of true 'mathematical modelling' occurred in Victorian times when a British mathematician (whose name I ought to remember but which eludes me at the moment) provided hangmen with instructions on how to carry out hangings, based upon the weight of the condemned person.
The objective of a 'clean' hanging is to fracture the second cervical vertebra, which results in death within a very short time. If the rope is already taut when the trap door is opened, the vertebra is not fractured and the victim dies through strangulation. This can take several minutes.
So it's better that the rope is slack when the trap door is opened, so that the victim accelerates downwards until there is a sudden pull on the neck which fractures the second cervical vertebra. However, if there is too much slack on the rope (and with a long enough drop below), there is a strong risk that the descending body will have accelerated to such a high speed, before the rope suddenly tightens, that the head will be wrenched from the body.
Both of these problems (strangulation and beheading) occurred in British judicial hangings until the mathematician calculating figures for the correct length of slack rope for victims of various weights.. Thereafter, there were no reports of either strangulation or beheading occurring when people were hung in British prisons.
It seems that the Iraqi authorities don't know about mathematical modelling. (It's also sad that all this stuff about hanging is just about all I can remember from my degree course in mathematics!)
Chris