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Hi Birger, First, I would like to say that this logo drew my attention to it right away from afar; compared to the others displayed. Secondly, I have to admit I was having fun looking at the unique shapes and was floored when I read that it was supposed to be a b and d.
So, I think the best way to handle this one would be to make the stem longer on the top part of the b and the d. Then I'm not really sure if this one could stand alone and would need the name of the company under it so relation is clear on the b and d. Then after awhile it may stand on it's own recognition. I think if you add a back to the b and d that you will lose the beauty of this a bit. Yet, it may be worth trying for the clarity of it.
Is the bottom of your "b" the right width compared to the front of the "b"? it looks a bit thinner... thus throwing off the grey triangle a bit ( compared to the others).
I like the colors used.

Thanks for the nice comment! As mentioned before, I will give it a go (the larger stem). Yes, both widths are the same, but because it's a false perspective (not a proper 2-points perspective), it looks a bit odd. I will make a new version in a proper 3D-program.
Also I think your comment about the missing company name is correct. I recently read an interesting article about logo design (link: http://speckyboy.com/2010/09/09/eight-helpful-rules-for-logo-designers/), I will try and make a new design keeping your wonderful suggestions in mind!
Thanks!