  New methods are introduced for the description and evaluation of tree-level
gravitational scattering amplitudes. An N=7 super-symmetric recursion, free
from spurious double poles, gives a more efficient method for evaluating MHV
amplitudes. The recursion is naturally associated with twistor geometry, and
thereby gives a new interpretation for the amplitudes. The recursion leads to
new expressions for the MHV amplitudes for six and seven gravitons, simplifying
their symmetry properties, and suggesting further generalization. The N=7
recursion is valid for all tree amplitudes, and we illustrate it with a
simplified expression for the six-graviton NMHV amplitude. Further new
structure emerges when MHV amplitudes are expressed in terms of momentum
twistors.
