Ouch!

Saddam Hussein's half-brother was decapitated during his execution by hanging.

The guards in charge of the execution used rope that was too long, was the problem. There's actually a mathematical formula that executioners are supposed to follow that takes in the condemned person's weight, height etc. and from that it spits out how long the rope should be. Too short and the guy dangles there and slowly suffocates. Too much rope and it takes the poor sap's head clean off. Ideally, the drop is abrupt enough to violently break the condemned's neck so as to bring about unconsciousness as quickly as possible.

There are some things you learn in history class that you can't "unlearn", if you know what I mean...