We show how to compute the maximum path length of binary trees with a given size and a given fringe thickness (the difference in length between a longest and a shortest root-to-leaf path). We demonstrate that the key to finding the maximum path length binary trees with size N and fringe thickness Δ is the height h Δ, N = ⌜log 2((N + 1)(2 Δ − 1)/Δ)⌝ . First we show that trees with height h δ, N exist. Then we show that the maximum path length trees have height h Δ, N − 1, h Δ, N , or h Δ, N + 1.