IKEA has two models of desk organizers. One is made of cardboard, cheap and is pretty big. The other is more elegant in size and material with a faux leather look. It also costs about twice as much. I opted for the cheap one, as I had enough space on my desk to fit it in. However, due to its big size, the papers stored in the rear room folded under their own weight and got crumbled. Also, any other tall things stored in the rear room stood the risk of tipping over making them hard to reach.
To fix this, I designed a simple divider made of a few pieces of laser cut plywood, I found in the leftover drawers, notched together.
Initially the divider consisted simply of a cross dividing the big rear room into one ~24 cm wide for storing A4 paper upright, and the remaining ~10 cm for storing other things. I made the divider for the smaller compartment a bit lower, so things didn't get lost in it.
Upon installing it, I found that the long end was flopping around, making it unstable and difficult to work with. To remedy this, I took the piece back to the laser cutter and cut a new notch at the far side of the long room, to put another piece into. With one long piece and two short pieces, the whole thing is perfectly stable and works as intended.