One anesthetic/deep sedation that you could ask for is Propofol. Amongst other things (besides being an excellent anesthetic, something both observed and experienced when I got my kidney stone out), Propofol has an amnesic side-effect so that memory of the procedure itself is at worst very blurry, at best non-existant. It can be used for 'deep sedation' procedures, where the patient isn't anesthetised (completely asleep), is rather deeply sedated (will rouse to strong stimulation, otherwise out of it).