  We consider a class of compact homogeneous CR manifolds, that we call
$\mathfrak n$-reductive, which includes the orbits of minimal dimension of a
compact Lie group $K_0$ in an algebraic homogeneous variety of its
complexification $K$. For these manifolds we define canonical equivariant
fibrations onto complex flag manifolds. The simplest example is the Hopf
fibration $S^3\to\mathbb{CP}^1$.
  In general these fibrations are not $CR$ submersions, however they satisfy a
weaker condition that we introduce here, namely they are CR-deployments.
