My box is 4" and the deck just barely sits flush, and if anything is 1/8"-1/4" too tall. Others with similar boxes reported the same. I used a cardboard box to test fit before I cut any wood so you might try that before building.Correct me if I'm wrong, but I measured the height of where the lid would rest on the ledges and I get 4.5". Is the middle higher than the edges for clearance? I know it's only .5" but every little bit helps.