  We study ruled orders. These arise naturally in the Mori program for orders
on projective surfaces and morally speaking are orders on a ruled surface
ramified on a bisection and possibly some fibres. We describe fibres of a ruled
order and show they are in some sense rational. We also determine the Hilbert
scheme of rational curves and hence the corresponding non-commutative Mori
contraction. This gives strong evidence that ruled orders are examples of the
non-commutative ruled surfaces introduced by Van den Bergh.
