  We study derangements of $\{1,2,\ldots,n\}$ under the Ewens distribution with
parameter $\theta$. We give the moments and marginal distributions of the cycle
counts, the number of cycles, and asymptotic distributions for large $n$. We
develop a $\{0,1\}$-valued non-homogeneous Markov chain with the property that
the counts of lengths of spacings between the 1s have the derangement
distribution. This chain, an analog of the so-called Feller Coupling, provides
a simple way to simulate derangements in time independent of $\theta$ for a
given $n$ and linear in the size of the derangement.
