  Let X=G/K be a connected Riemannian homogeneous space of a real Lie group G.
The homogeneous space X is called commutative if the algebra of G-invariant
differential operators on X is commutative. We prove an effective commutativity
criterion and classify commutative spaces under two mild technical constraints.
In particular, we obtain several new examples of commutative homogeneous spaces
that are not of Heisenberg type.
