The "humane treatment" used by many animal control/welfare agencies in the US is an anaerobic chamber, in which the air is pumpted out slowly, the animals lose consciousness painlessly, and continued evacuation of the air results in suffocation and brain death.

That this is quite painless to the victims subjects is substantiated by the requirement for "high altitude training and certification" for nearly all "test pilots" and for most military pilots.

Typically a group of candidate pilots are placed in a chamber and the "altitude" is raised. Somewhere above about 10,000 ft equivalent, a subject is told to remove his/her oxygen mask and tell a story. When the selected person passes out, the instructor slaps a mask back on them and they are immediately(?) revived and continue the story at precisely the same point where they lost consciousness. It is typically necessary to play back the video of the session before the subject who passed out will believe they were ever unconscious. (That they continue at precisely the same point where they stopped has been cited by some as proof that nothing happens and no "feelings" are perceived, while they are unconscious.)

A variation on this method has been recommended by advocates for terminally ill persons seeking advice on suicide. About all that can really be said about that variation is that no complaints have ever been voiced by anyone who used the method successfully.

John