Thanks for the warning.
I've seen these on the wiki, and was advised against them by a man with over 30 years expertise in mechanical engineering, since adding a second nut (From what I got there's already one under the piece of wood, correct if I'm wrong. I'll be disassembling it to have a look tomorrow). So in this way they can easily jam the threaded rod after a while. 
So I think of adding a custom-machined brass nut there with adjustment screws (Surely there's a nice translation of 'маточная гайка' to english, but 'uterine nut' that gogle translate suggests doesn't sound like something proper).
It will be a longer, but I hope the proper way, if I manage to find a 5/16 screw tap here (all the stuff I have is metric, and regular M8 I have around don't fit).

I think this is the reason some people use a spring between the two nuts (with a printed part to hold the top nut from turning).  This way there is constant spring force pushing down on the bed. 
This is what I have done (added the spring) and it seems to work well. 
This is functionally the same as adding weight to the bed, except the weight is pressing directly on the nut instead of being on the bed and possibly warping the bed or something.

I don't have it done to mine, but from the way I understand it by placing the printed piece over it you are locking the distance between the lower nut and the new nut.  They have to rotate together and so they can't rotate closer to each other and bind. 
"Uterine" nut is not the right translation.  Uterine is the inside wall of one of the lady parts.

Lol, somehow I knew that translation was a lie!
I thought about something like a split lead nut variation (That should be the proper translation) of something like 8-10mm height.

"Uterine" nut is not the right translation.  Uterine is the inside wall of one of the lady parts.

And a simpler version at Thingiverse - http://www.thingiverse.com/thing:36177

The one at Thingiverse might need a spring under the nut, because it requires the nut to be at a certain orientation which might not be the right amount of tension on your particular printer.

I went a slightly messier route- I tightened the 5/16-18 nut enough to remove the backlash, and then hot glued it into place.

Do a search on here for z wobble there are a number of proven fixes on here already.

I have come up with a (hopefully) better solution, but it will require to wait till the hardware shops open after the holidays here (in russia) are over. I will post the tests and the description of my second fix when I test it.