Actually, TB, the axe should not be flat like a chisel. Looking directly into the cutting edge, it should have a slight belly of 1/8th or so, like a gouge.

In my experience, there's no way to hew cleanly with a perfectly straight edge -- the corners dig no matter what you do.

I've also seen evidence of this in old frames. If you look closely at old hand hewn timbers, you can see that the axes were only cutting a swath a few inches wide with each stroke -- not the full length of the cutting edge.