Low profile bridge - what's out there?

I am working on a project fretless and would like to find a bridge with a low profile. The neck pocket is a little low on the body and a neck shim is required to get good action while using a Badass II bridge. Since that bridge is comming off for another project it would be nice to find one that is better suited for this bass.

If anyone is willing to measure their string height from the body at the lowest setting that would be real cool! I'm hoping to find something 11mm or lower (if it exists). Any speculative suggestions are also encouraged.

 

That's true, I might go that route if I don't find what I'm looking for.