Roof mounted, I would stay away from anything shorter than 12"...Personally I think the 17" shaft is perfect for roof mounting...22 and 27" shafts will tune lower on the roof, but are also easier to get broke off the roof because you have just too much solid antenna sticking up that wont bend out of the way if it hits something like a tree limb...(By the way, when a Predator 10K breaks, it's almost always at the base of the lower shaft where the studs at that screws into the antenna mount, I have yet to see one snap any place else)I'm still wrestling with the difference of a 22" vs 6", and all between, for mounting on my 4.5" Breedlove top dead center of my large rooftop.
years ago I did an experiment. I won't go into that here now.
6" and 9" lower shafts I have never-ever been able to get to tune worth a flip, and even had problems getting the 12" shaft to tune very good...But, if your flexible about where you want to put your mount, then you might find the right spot to use one of the shorter shafts...I've just usually have a spot all picked out for the antenna, then have to figure out how to get the things to tune where I want them.
This is a single-coil 10K on a 27" shaft that I had on top of my Suburban, until a low hanging phone line snagged it and snapped it off the roof and sent it flying...found the antenna about 75 yards off the road up in one of my neighbors front yard.