  The natural paramterization or length for the Schramm-Loewner evolution
(SLE{\kappa}) is the candidate for the scaling limit of the length of discrete
curves for \kappa < 8. We improve the proof of the existence of the
parametrization and use this to establish some new results. In particular, we
show that the natural parametrization is independent of domain and it is
H\"older continuous with respect to the capacity parametrization. We also give
up-to-constants bounds for the two-point Green's function. Although we do not
prove the conjecture that the natural length is given by the appropriate
Minkowski content, we do prove that the corresponding expectations converge.
