I have a pink fleece cover on my bed that leaves little fussy bunnys all over anything that touches it?

I had a beautiful chenelle white bedspread it looked so nice and was heavy it did the same thing I figure after I washed it it would nolonger leave lint but it did I gave it away but with your fleece blanket if its a bed size and not a throw why dont you put it inside a comforter cover or duvet after you wash it and you wont have the fuzz bunnies all over everything, just a suggestion