I like to use a plane and rasp until there is almost flat left on the back of the neck.
On some fretless builds I route the fingerboard with the same bit you use.,.,it makes it easier to hit the outer strings alone.,.,sort of like a violin.,.,for lighter strings you could thin the neck a little.,.,for heavier strings you need that 1 inch thickness.,.,unless you are using a truss rod, laminate neck, or using carbon fiber rods.,.,if you like thinner give it a try .,.,.no rules here.,.,
I meant "almost no flat"
Take a close look at the neck of any electric guitar and you'll see that it is very thin at the neck/headstock joint. That's a good indicator that you can thin out the neck quite a bit so that it's comfortable to play. If you are using a good hardwood for the neck (maple, mahogany, oak) then with only three or four strings, you are not stressing the neck if you thin it out.\
My current necks are 1 1/4" at the nut and 1 1/2" at the box I use a wood rasp to fully round the neck and thin it out so it feels good to play. A rasp for basic shaping and an 80 grit disk on a 5" sanding disk in a hand drill does the needed work in short order. No need to work up a sweat to get a nice neck shape.
Go ahead and thin that sucker out.
I shave my necks like this:
I do tend to thin the neck a little when I thin the headstock on the bandaw.
very cool! Thanks everyone for your ideas. I use hardwood. I guess I'm just not finishing the neck well enough. Thanks again everyone!
I have a spoke shave that I use to shape the back of the neck whether I add fret board or not. A router is a good way to remove a lot of material quickly and easily, but the resulting shape feels a bit chunky. A spoke shave is a hand tool but works quite quickly even at a shallow depth. You could also easily taper the thickness along the length with it if you like.
Keep in mind, unless you have a truss rod you can't thin the neck too much or it will box under stress, especially with a 4 string. That said, a spoke shave allows you to sculpt exactly the shape you want: round, D-shaped, V-shaped, whatever. I have one guitar with a 1/4 fret board that is V-shaped; the fretboard gives it a lot of thickness so it's not bowing. I have a 4 string with no fret board built from a 1x2. I rounded the back but left as much material as I could to keep it from bowing.
Even with this method, if I leave the slightest bit of flat from the original board on the back you can instantly feel it when you grab the neck. It takes a delicate hand to cut out all the flat and leave enough mass to no bow.