accuracy and effectiveness essentially disappear with the shortest barrels.
Most stagecoach security guards shortened their barrels some to get better follow through and to get the weapon into action sooner.
The truly short sawed offs were carried under coats or in holsters by those who were poor shots with pistols for up close work, usually in anticipation of sudden altercations.
Remember that the early blackpowder shotguns often had long barrels for game-getting, but were cumbersome for self defense. As someone else noted, the plethora of firearms today make a truly short shotgun pointless -
and VERY illegal.