Rounding edges of a non uniform mesh

Question

Given this hinge:

I would like to round the 2 edges closes to the opening, without rounding the inset edge.

The aim is to model a wooden hinge such as this:

.

I have looked at beveling, but it does not have the desired effect.

Answer 1

I think beveling is a good option. Select the edges as pictured below, press Ctrl+B and drag the cursor in opposite direction to the edges' location. Use Mouse Scroll to add some divisions. Finally change the rest of the mesh topology to easily add a Subsurf and edge creases.

Here's the final result with a changed topology.

And here's the .blend with improved topology: