How do I fix movement in headset I have bought a second hand bike and generally it's going well. However, there is a small amount of play in the headset that I've been trying to diagnose and resolve.

It's a threadless fork.

I've adjusted the tension by loosening the headstem bolts and tightening the top cap. I tighten it up a lot and this reduces the play a little, but when I brake hard or hit a bump I still get the 'clonk' as it moves to the limit of it's adjustability.

I've used this article on Sheldon Brown for the terminology I use below, particularly this photo:



I've taken some photos and have an idea of what the problem is. In this photo I've laid out from left to right the dust ring, followed by the compression ring.



When the compression ring is placed on the steerer tube, there is slight gap between them. It's maybe a millimeter, although I don't have anything to measure that with here. Watching the movement carefully I'm quite confident that it's this gap that's causing the steerer tube to clonk around.



I've measured the steerer and it's 28.6mm which is 1 1/8" according to Sheldon's site linked above.

So why is there a space around the compression ring? What's the best way to resolve this? Do I just need to find a smaller compression ring somehow? Or is there something I'm missing?

Updated: Added text to photo



Update

I think I'm missing a part. If you look closely at the exploded graphic from Sheldon, the compression ring has a gap in it, allowing it to shrink onto the steerer tube and hold it firmly. My compression ring is solid, so nothing can shrink and grip. Kudos to Zen as well, since he mentions that it's a wedge. I'm going to have a look around at home to see if I can find the missing bits. Otherwise a new headset should sort it. Thanks all!
The compression ring is a wedge.  There will always be space and movement here, until the headset is assembled and adjusted.

It looks like you're missing a part. There should be another hoop with a wedge shape and a split. It's the split ring on the upper left in the image below. This part is what grips the steerer tube tight and will eliminate the clonking you're experiencing.





If you are confident that all the parts are there, and assembled in the correct order, then you have 3 likely reasons for movement:  


The first is that there is damage to the bearing cartridges.  This can show as movement when adjusted correctly, although usually on a headset it will fail first by being rough or crunchy feeling.
Secondly, there may be movement between the frame and the headset cup, which can mean that the frame is in need of replacement.  This can't be fixed via adjustment.  There are ways to attempt a fix, but it is best looked at by a qualified mechanic, first.
Last, there may be no movement in the headset, but you could be feeling movement in the brakes, depending on how you are checking for movement.  Try checking for movement by standing the bike on the rear wheel, turning the handlebar all the way to the left or right, and checking for movement with your hand around the headset.  That way if it is in the headset, you will feel it directly.


I hope that is helpful.