  We consider the point-indentation of a pressurized elastic shell. It has
previously been shown that such a shell is subject to a wrinkling instability
as the indentation depth is quasi-statically increased. Here we present
detailed analysis of this wrinkling instability using a combination of
analytical techniques and finite element simulations. In particular, we study
how the number of wrinkles observed at the onset of instability grows with
increasing pressurization. We also study how, for fixed pressurization, the
number of wrinkles changes both spatially and with increasing indentation depth
beyond onset. This `Far from threshold' analysis exploits the largeness of the
wrinkle wavenumber that is observed at high pressurization and leads to
quantitative differences with the standard `Near threshold' stability analysis.
