Thanks for the tip Adam!
Sketch And Toon works a lot better!
But!
When the 'edges' checkbox is checked it, once again, get's messed up. I'm wondering if it all comes down to it being the .eps that is causing the trouble.
I think I will leave it at this. But it would be interesting to know what is really causing this problem.
So if anyone have any further ideas - please, let me know.
And thanks for the help!