  We extend our recent results on propagation of semiclassical resolvent
estimates through trapped sets when a priori polynomial resolvent bounds hold.
Previously we obtained non-trapping estimates in trapping situations when the
resolvent was sandwiched between cutoffs microlocally supported away from the
trapping, a microlocal version of a result of Burq and Cardoso-Vodev. We now
allow one of the two cutoffs to be supported at the trapped set, giving
estimates which are intermediate between the trapping and non-trapping ones.
