As nice as bandsaw is, bandsawPro is nicer.

Here's a good situation for it: I'd like the division to tend towards one edge or the other.
Click [n] to open the tool's numeric panel and simply drag the slider!
Now I assign surfaces and shift my 'sk_mouth' polygons inward. The 'sk' is for 'skin' and eases future surface selection and editing.
Tweak. I need more detail for my nose (hehe), so I select polys from the brow down to the inner upper lip.
I then do the following:
- smooth-shift
- deselect the bottom polys and
- stretch the remaining polys downward and inward.
Because the deslected points haven't moved from their source geometry, I can merge them at the click of the [m] button
This is what it looks like in perspective. Above after the smooth shift, below after deselecting and stretching.
Now open the statistics window [w] and select the 2-point polys.
We have quickly and efficiently created the geometry necessary for my pointy lips! Tweak 'em and off to my nose, the highlight of my face!
Above, before and after a simple spinQuad operation. This is much better for the contours of a brow.