Before revision:  First, we use Catalan numbers and a restricted version of the Window Movie Lemma (Meunier, Patitz, Summers, Theyssier, Winslow and Woods, SODA 2014) to prove two new lower bounds on the minimum number of unique tile types required for the self-assembly of rectangles. We then give a general construction for the efficient self-assembly of thin rectangles. Our construction is non-cooperative and " just-barely " 3D in the sense that it places tiles at most one step into the third dimension.
After revision:  First, we use Catalan numbers and a restricted version of the Window Movie Lemma , we derive a new lower bound on the tile complexity of thin rectangles at temperature-1 in 2D. Then, we give the first known upper bound on the tile complexity of `` just-barely " 3D in the sense that it places tiles at most one step into the third dimension.