His elder son, Uday, and younger son, Qusay, played such legendary roles in Iraq's iron fist rule that their hold over people continued even while they were at large.
There appears to have been a view among ultra-loyal Baathists that, while all three were alive, there was a possibility that things could be made unbearable for the coalition forces and the old regime could return.
However distant that prospect, it was enough to instil among others the fear of terrible retribution.
Symbolic
They had seen it happen when the regime's forces hit back after the uprisings that accompanied the 1991 Gulf War. While Saddam Hussein remains on the run from the coalition, there could be some Iraqis still unwilling to set those fears aside, or indeed some who would still cling to the notion of his return.
But the killing of his two all-powerful sons is so symbolic that it can only be hugely disheartening for the arch-loyalists.