  We present a new approach to the intrinsic properties of the type D vacuum
solutions based on the invariant symmetries that these spacetimes admit. By
using tensorial formalism and without explicitly integrating the field
equations, we offer a new proof that the upper bound of covariant derivatives
of the Riemann tensor required for a Cartan-Karlhede classification is two.
Moreover we show that, except for the Ehlers-Kundt's C-metrics, the Riemann
derivatives depend on the first order ones, and for the C-metrics they depend
on the first order derivatives and on a second order constant invariant. In our
analysis the existence of an invariant complex Killing vector plays a central
role. It also allows us to easily obtain and to geometrically interpret several
known relations. We apply to the vacuum case the intrinsic classification of
the type D spacetimes based on the first order differential properties of the
2+2 Weyl principal structure, and we show that only six classes are compatible.
We define several natural and suitable subclasses and present an operational
algorithm to detect them.
