Almost any additional punishment would reduce crime. The question is is it worth it?

I meant that it would reduce crime by an amount greater then the amount of suffering the punishment generated.

For example, suppose a man gets fed up and goes on a killing spree, ultimately ending in suicide. However, he has a daughter that he care about and you (somehow) know that he would have been less inclined to go on a killing spree if he thought his daughter would be punished as a result. Would you favor punishing the daughter?

I think punishments are probably too harsh generally.

Are you sure this isn't just because the image of a harsh punishment is more available then a vague dispersed deterrent effect? Keep in mind, the harsher the punishment, the more effective the deterrent, the less the punishment actually gets carried out.