Can the State Inflict Pain?

A serial killer of children was executed in Iran, with the victims' family members participating in a slow and brutal process of stabbing, flogging, and hanging.  Eugene Volokh embraces this approach:

I particularly like the involvement of the victims' relatives in the killing of the monster; I think that if he'd killed one of my relatives, I would have wanted to play a role in killing him. Also, though for many instances I would prefer less painful forms of execution, I am especially pleased that the killing — and, yes, I am happy to call it a killing, a perfectly proper term for a perfectly proper act — was a slow throttling, and was preceded by a flogging. . . . I am being perfectly serious, by the way. I like civilization, but some forms of savagery deserve to be met not just with cold, bloodless justice but with the deliberate infliction of pain, with cruel vengeance rather than with supposed humaneness or squeamishness. I think it slights the burning injustice of the murders, and the pain of the families, to react in any other way.

Putting the question of capital punishment to the side, is there any basis in Catholic legal theory for seeking to inflict pain in our punishment of criminals?  According to the Compendium of the Social Doctrine of the Catholic Church (para. 402), the state "has the twofold responsibility to discourage behaviour that is harmful to human rights and the fundamental norms of civil life, and to repair, though the penal system, the disorder created by the criminal activity."  And in correcting the offender, punishment is to encourage "the re-insertion of the condemned person into society," and foster "a justice that reconciles, a justice capable of restoring harmony in social relationships disrupted by the criminal act committed." (para. 403)

Given these objectives, is punishment to be as painless (physically, mentally, and spiritually) as possible, or in fulfilling its duty to discourage improper behavior, especially monstrous behavior, does pain have a place?

Rob