  We prove better Strichartz type estimates than expected from the (optimal)
dispersion we obtained in our earlier work on a 2d convex model. This follows
from taking full advantage of the space-time localization of caustics in the
parametrix we obtain, despite their number increasing like the inverse square
root of the distance from the source to the boundary. As a consequence, we
improve known Strichartz estimates for the wave equation. Several improvements
on our previous parametrix construction are obtained along the way and are of
independent interest for further applications.
