[Gizmo2]

How big is a small lean-to?

 

[Gizmo2]

That's probably more proper than what I do. I usually just set a rafter on the top plate and use hurricane ties without cutting those out.

I've done it both ways but prefer not to do the cuts.
On a small pole building/lean-to I run boards across the poles, set the rafters and then run another set of boards across the poles on the otherside, pushing it up until it meets the rafters.

 

[Gizmo2]

I would suggest 6x6 as opposed to 4x4 for longevity, strength, and resistance to bumps/accidents. Birds mouths are easy to cut and figure out as well as providing a more stable rafter, making easier to nail and spreading the load, are you in a snow zone?

I can't disagree with any of that.