In the spirit of this Finnish IT retailer listing most returned products, for once, this is not really an howto. The easiest solution I found was to return it. The contrast and luminosity is impossible to set. It changes over reboot, it changes over operating system. And even set to get high contrast, black is never black, despite Iiyama claiming that “it is also possible to adjust the brightness and the dark shades with the Black Tuner, giving greater viewing performance in shadowed areas”. I replaced it with a SyncMaster S24D340H and had none of these problems.
Side note: I also had a defective pixel, but that could happen I assumed. Well, turns out that out of 16 comments of the shop, 4 report 0 day defective pixels.