three cube reflection map scaling

I've spent some time researching this and playing with parameters, but cannot seem to get it working right.

I have a cube geometry in Three.js scene that is using a reflection environment map (Park from Three.js examples http://ift.tt/29IGH9f). The size of each of the textures in the environment map is 2048x2048.

I notice that if my cube is rather small the reflection in it looks very pixelated.

For instance this is the cube of size 16x16x16

On the cube of size 1600x1600x1600 the reflection looks almost as good as the images used for the environment map.

What are my options, if any, to make the reflection look better on small objects like the first cube. I understand that environment map is assumed to be infinitely far away, so perhaps it plays into the issue. Can I set the size of the environment map or scale textures?

Thanks in advance for your help.