Most libertarians believe that death penalty is an extreme exertion of state power and is of little use in a free society, while it is of great use to tyrants. Some libertarians believe that punishment is justified as a deterrent to particularly atrocious crime and dangerous individuals need to be permanently incapacitated.

Many libertarians, including most anarcho-capitalists, believe that penal justice in general should not exist, but only retributive justice. To them, the death penalty shouldn't exist, just like no penalties should exist but only retributions.

On the other hand, libertarians believe in the right and occasional necessity to resort to violence for police purpose; to them, if an outright criminal cannot be otherwise made to stop his criminal behaviour, then he might justifiably be killed.

In any case, to anarcho-capitalists, making judges, policemen and other law enforcement people just as responsible for their acts as any citizen, with no privilege or special right or exemption, will prevent abuse of force in general, and of deadly force in particular.