Well, I had a stash of preemie prefolds that were too small for DS from the get-go, but they found an alternate life...as boob diapers. I lay either a fleece blanket or a towel on the bed (which has a sheet over a waterproof mattress pad), and do one of 2 things. Either I keep my T-shirt with the 2 folded in half preemie prefolds stuffed in it (one over each nipple) on, and just pull up the lower one to feed DS, or I go shirtless and tuck a preemie prefold between the 2 to catch whatever drips out of the top one. At first I was going through a lot of them; now I'm not as drippy (2nd go round seems to be going that way for me), but while nursing on one side, the other side always drips. At first a preemie prefold under DS's face where it met my breast was also helpful. I was changing out the towel/blanket every day at first, now I'm down to every three or four days.
I recall with DD, when I was much drippier, I would actually sleep with a premium (large) prefold stuffed into either a nursing bra or a T-shirt, and change it out when I changed DD's diaper.
So to summarize: use cloth diapers.