  This article studies the poset of simple permutations with respect to the
pattern involvement. We specify results on critically indecomposable posets
obtained by Schmerl and Trotter to simple permutations and prove that if
$\sigma, \pi$ are two simple permutations such that $\pi < \sigma$ then there
exists a chain of simple permutations $\sigma^{(0)} = \sigma, \sigma^{(1)},
..., \sigma^{(k)}=\pi$ such that $|\sigma^{(i)}| - |\sigma^{(i+1)}| = 1$ - or 2
when permutations are exceptional- and $\sigma^{(i+1)} < \sigma^{(i)}$. This
characterization induces an algorithm polynomial in the size of the output to
compute the simple permutations in a wreath-closed permutation class.
