  We present radio and submillimetre observations of the O4I(n)f star zeta Pup,
and discuss structure in the outer region of its wind (~ 10-100 R*). The
properties of bremsstrahlung, the dominant emission process at these
wavelengths, make it sensitive to structure and allow us to study how the
amount of structure changes in the wind by comparing the fluxes at different
wavelengths. To look for variability, we acquired 3.6 and 6 cm observations
with the Australia Telescope Compact Array (ATCA). We supplemented these with
archive observations from the NRAO Very Large Array (VLA). We did not find
variability at more than the +- 20 % level. The long integration time does
allow an accurate determination of the fluxes at 3.6 and 6 cm. Converting these
fluxes into a mass loss rate, we find Mdot = 3.5 x 10^{-6} Msun/yr. This value
confirms the significant discrepancy with the mass loss rate derived from the
Halpha profile, making zeta Pup an exception to the usually good agreement
between Halpha and radio mass loss rates. We also observed zeta Pup at 850 mum
with the James Clerk Maxwell Telescope (JCMT) and at 20 cm with the VLA. A
smooth wind model shows that the millimetre fluxes are too high compared to the
radio fluxes. While recombination of helium in the outer wind cannot be
discounted as an explanation, the wealth of evidence for structure strongly
suggests this as the explanation for the discrepancy. Model calculations show
that the structure needs to be present in the inner ~ 70 R* of the wind, but
that it decays significantly, or maybe even disappears, beyond that radius.
