I've had a hard time with the handlebar mount for my Niterider Lumina 650. Basically it just won't camp down on my 31.8 bars tight enough to keep from moving. I can't use the rubber shim (too big) and the threaded knob just slips off of the end when I tighten it enough causing the mount to come off. I'm left with a semi-loose mount that I constantly have to monitor. On the other hand I also have a PDW light and the mount is awesome. I ended up with an extra mount from each and decided to swap the rails and see if it would fit. After cutting off the "button" under the rail of the NR and screwing it down onto the PDW mount I found that a washer and some filing of the screw was needed for clearance. A little bench work and voila! And yes, still swivels. Cheers!

i had a similar problem with my minewt 350. i have the older style handle bar mount. it was too big for my handlebars. i tried shimming it with an old innertube but it wasn't enough. i sent an email to niterider's customer service explaining my problem and they sent me the new style clamp for free, the same one you have pictured. i didn't even know there was an updated version. i just got it last week. it looks to be smaller diameter. i haven't tried it yet. the old one doesn't work on anything i have.

edit:
i just tried the new clamp. it's the same size as the old one, but the thumb screw allows me to tighten it down more so i think it'll work just fine.

They sent me one too when I told them the one I had didn't fit. They said it would fit the 31.8's but it ended up being the same mount I already had. I even sent them a pic of the PDW mount showing the better fit so maybe they'll do a redesign. Until then the modified PDW is working well.

My Cygolite ExpiliOn 700 came with a similar mount, but the knob is longer and easier to tighten/loosen by hand. It works awesome on my 31.8 drop bars.

A thinner shim, like a piece of inner tube or something would work?

It doesn't fit well with all of the shims removed. Adding a thin one would make it worse. There's just no room for it.

One or three wraps of electrical tape worked for me.

I guess I wasn't clear enough about the mount. The nite rider doesn't fit the bar even though they say it fits up to 31.8. Sticking any material between the mount and the bar is just going to make it worse. Think of it as shoes that are too small. Wearing thin race socks instead of bulky hiking socks still won't make them fit any better. :-)