Thanks to a conversation with Vivek, I dug up three old Pentax 110 lenses (18mm, 24mm and 50mm) and am trying them on the A7R. You can get these lenses for about $15-20 each. I'm using an inexpensive Fotasy adapter.
They are the cutest little lenses you ever saw.
And I'm surprised at how well they work. To my amazement, all three can cover the APS-C image area with only minor falloff. This yields a 15MP image. There's no aperture, so you have to shoot at ƒ2.8 all the time.
Here's the 18mm mounted on the camera, a snapshot with that same lens, and a 100% center crop from another shot.