Will my chenille bedspread ever stop shedding?

I bought a fairly heavy-weight chenille bedspread that I just adore. I knew it would shed some, but it is really getting everywhere. EVERYWHERE. I've washed it a couple of times, and also toss it in the dryer on air fluff for an hour or so a week. This always removes a lot of lint, but it just seems never-ending. I don't remember the ones I had as a kid shedding like this. It is 100% cotton. Any suggestions?