  We consider Morawetz estimates for weighted energy decay of solutions to the
wave equation on scattering manifolds (i.e., those with large conic ends). We
show that a Morawetz estimate persists for solutions that are localized at low
frequencies, independent of the geometry of the compact part of the manifold.
We further prove a new type of Morawetz estimate in this context, with both
hypotheses and conclusion localized inside the forward light cone. This result
allows us to gain a 1/2 power of $t$ decay relative to what would be dictated
by energy estimates, in a small part of spacetime.
