  We prove the following: (1) if $X$ is ordinary, the Fulton-MacPherson
configuration space $X[n]$ is ordinary for all $n$; (2) the moduli of stable
$n$-pointed curves of genus zero is ordinary. (3) More generally we show that a
wonderful compactification $X_\sg$ is ordinary if and only if $(X,\sg)$ is an
ordinary building set. This implies the ordinarity of many other well-known
configuration spaces (under suitable assumptions).
