Pickup hiss only while the tone is played and sustained

[diego]

OK, I have this problem, and I'm not sure how "normal" it is with soundhole pickups, so I'll fire away:

I've mounted Woody Seymour Duncan pickup, and while the tone is great and to my liking, without any actual noise while I'm NOT playing, whenever I pick a tone or struck a chord (doesn't mind if it's open or fretted tone) I can hear the background sort of hiss/buzz as long as the actual tone is sustained. Doesn't matter what kind of amp I'm using. The hiss fades away with the actual tone. It's not that noticeable when the amp is on low volume, but as the volume goes up high it becomes obvious. That problem is not occurring on the same guitar when I'm using the piezzo system. Any thoughts? This "problem" reminds me of the time I used floor processors for the electric guitar, and they would produce the same kind of hiss when the tone is played. Is pickup at fault, or is each one bound to have this?