Area light rings artefact (maybe caused by small light size)

I was trying to make soft shadows with a Blender 2.37a area light, and found a strange artefact:

This stripped down scene has a large plane with default material, an area light with size = 0.11, and a camera. Raytracing is off, but turning it on and using rayshadows with multiple samples does not help.
It seems to be caused by the small size of the area light.

I would be interested ways to avoid the artefacts while keeping the area light small, so the shadows are not too blurry.

Here is the .blend with an animation of the light moving set up just for fun:

It will probably be easiest for me to just switch from a ray traced area light to a spot light with shadows.

Here’s how the artefact looked in a scene, notice the slightly-too-soft shadows.