I earlier mentioned that I'd tried different brands of headphones with the same result. Today I tried a cheap old Phillips Headphone, and the hiss was gone! I then borrowed a more expensive Sony, and the same result: No hiss at all, even with the volume turned all the way up! But when I swithced back to my own phones of the brand "db" and "Koss", the hiss was back.

Could it be that the impendance of my headphones was wrong? I noticed that I couldn't get as much volume in the headphones that worked OK as I used to get in my own headphones.

Glad that I discovered this before I returned the keyboard. Now I'll just have to test som new headphones to make sure I got a pair that works...