Any discussion about the death penalty would be lacking if it did not look into the method.
I think we are all far enough advanced to agree that if the death sentence is passed, that execution should be as quick and painless as possible, so it is necessary to examine a few methods.
Shooting is not very quick. The arrangements for securing the intended victim loading the weapons and keeping everyone safe generally means that execution will not complete sooner than 20 minutes after the condemned has been brought out of their cell. Successful execution depends on the accuracy of the shots and even though every shot passes through the heart, death is not that instantaneous. The victim will experience very great pain as the rounds enter the body and only the shock induced by the violence and pain, may cause rapid loss of consciousness.
Beheading, is very quick and can be carried out safely within less than a minute after the condemned is brought from their cell. Death will be through loss of blood supply to the brain though it is not certain the head striking the ground is not felt. Death by the sword or axe, depends on the accuracy and skill of the headsman and occasional misses have caused untold suffering before the head finally cams off. A guillotine is much more certain, but does require the victim to strapped down which adds to the time and consequent agitation for the victim.
Electrocution is very quick if sufficient voltage passes through the victim's body, but this depends on good electrical contacts and all too often the victim has been burned before they expire, because there was not a good connection between the victim and the voltage, because the victim may have been dehydrated, or because the electric chair itself was faulty.
Lethal Injection is thought to be the soft option, but like the electric chair depends on gadgetry working properly. On occasions the first of the three syringe drivers has become stuck, so that the heavy sedative element is not given before the more painful lethal elements are pushed into the bloodstream. This can be a very painful way to go.
Gassing is a very complicated affair and is a long and drawn out process. The victim must be strapped to a chair, so they cannot run around in a panic. The cyanide gas can easily condense into droplets on coming into contact with surfaces which are not heated to 25 degrees. The gas will revert to it's liquid form below 25 degrees C. The droplets are highly explosive and are equivalent to nitro-glycerine. A panicking victim could could easily caused an explosion which would blow the gas chamber apart and kill everyone near to it. The gas chamber itself is heated and the victim must be strapped into a chair, the heavy steel door is closed from the outside and a 10 inch vacuum is drawn by extractor fans, before the potassium cyanide pellets are dropped into the sulphuric acid. A four inch vacuum will make your ears pop. Death may not occur until 20 minutes have passed. Poisoning by cyanide is an extremely violent affair as the body contorts and the victim suffers terrible hallucinations, through oxygen starvation to the brain.
Death By Hanging can be very quick. Albert Pierpoint the British hangman once recorded a time of 8 seconds between entering the condemned cell and the victim swinging at the end of the rope. His method was the long drop of between 6 and 8 feet depending on the victim's weight, strength of neck and shoulder muscles. The noose is passed over the head with the standing part across the throat. The trap door on which the victims stands open and they drop through, the noose tightening as it takes the weight of the body and the heavy brass thimble through which the rope passes comes round and under the chin forcing the head back and snapping the neck, hopefully between the first and third cervical vertibrae. When a female is hanged the shock of the body being suddenly arrested by the rope after an 8 foot drop will likely cause prolapse of the uterus.
There are shorter drop methods but they require the intervention of the hangman who must ensure the neck breaks appropriately.
In Iran the state uses the slow lift when it hangs it's victims. It may be thought that this is quite barbaric, but having watched a number videos of such executions I am satisfied that this is actually the most humane method of execution. Almost as soon as the weight of the victim is taken by the rope, unconsciousness sets in as the noose tightens. Death can be certified after 20 minutes, though strong pressure on the carotid sinus can quickly arrest breathing and stop the heart. The so called dance of death is due to circulation running down and the nerves starved of oxygen cause the limbs to jerk slightly, resulting in a swaying motion with the body circling slowly at the end of the rope.
Garrotting is probably as quick and relatively painless as the slow hanging method. My study and understanding of martial arts strangulation, leads me to believe that slow hanging or garrotting is about the least painful method of execution.