I created a space where they could save their favorite things.
I took big clear plastic tubs that fit under my kids' beds, and told them they could store anythings they want in there (within reason!). Tests that have spent their day in the spotlight (aka on the refrigerator), but are too important to toss, are now stored in tubs I was formerly using for the storage of clothes the kids had outgrown. A trip to Goodwill later, the kids can fill the bins with assignments, reports, notes from friends, treasured coloring book pages, or whatever it is that I don't want to display, but is special enough that they don't want to part with it. The bins slide out from under each of their beds, so the kids can access the contents any time, but it's all out of sight, so their mom doesn't lose her mind!