AH! A historical question! Ya got your short drop (with horses usually), your standard drop (about 6 feet), and your long drop (based on height and weight). Then ya got your gallows or a gibbet.
Our museum in Gensee county, NY has a Gibbet on display. It used the counter balance method. Gallows -- floor drops, guy falls. Gibbet - The condemened stands on the ground. A weight was held by a bracket. Bracket is released, weight falls, guy is yanked up.
I have a true crime from the 1850s (self published) "Bread & Butter: The Murders of Polly Frisch. A gibbet is how my murderess would of hung in that county had her sentence not benn commuted to imprisonment for life.
I've researched all the hangings in Genesee County actually. (Hey, its history) They were very graphic in the newspaper, checking the pulse every few minutes, then just waited. Then there is the tickets,can't forget those. You needed a ticket to attend. (I got a copy of one in my files) Plus the whole religious aspect. At least around here. One guy swore he was an atheist, and it delayed his hanging for a month. Lots of good creative writing stuff you can do with a hanging.