CrossRoads:
You really want chips like TLC5490, WS2803, shift in PWM data and let the chip control the LED current.
Thanks for your reply!
Okay so happy to find out that I'm not completely stupid here 
I asked in the store for the TLC5490 as that seems to be what people are using, but they had none of those in stock and gave me these in stead... Hmm... I'll pay them another visit!
Thanks.
/ Simon