Every (n+1)-dimensional lattice is built up of layers of n-dimensional lattices. An (n+1)-dimensional laminated lattice is built up of layers of n-dimensional laminated lattices packed as densely as possible. Thus, the definition of a laminated lattice is recursive, and what counts as a laminated lattice in n dimensions depends on what happens in all the lower dimensions. The process of "laminating" lattices can be viewed as a "greedy" way of constructing dense lattices. In some dimensions, this construction yields the densest possible lattices; in other dimensions, there are denser lattices that cannot be constructed in this way.