  We have modelled the circumstellar envelope of {\it o} Ceti (Mira) using new
observational constraints. These are obtained from photospheric light scattered
in near-IR vibrational-rotational lines of circumstellar CO molecules at 4.6
micron: absolute fluxes, the radial dependence of the scattered intensity, and
two line ratios. Further observational constraints are provided by ISO
observations of far-IR emission lines from highly excited rotational states of
the ground vibrational state of CO, and radio observations of lines from
rotational levels of low excitation of CO. A code based on the Monte-Carlo
technique is used to model the circumstellar line emission.
  We find that it is possible to model the radio and ISO fluxes, as well as the
highly asymmetric radio-line profiles, reasonably well with a spherically
symmetric and smooth stellar wind model. However, it is not possible to
reproduce the observed NIR line fluxes consistently with a `standard model' of
the stellar wind. This is probably due to incorrectly specified conditions of
the inner regions of the wind model, since the stellar flux needs to be larger
than what is obtained from the standard model at the point of scattering, i.e.,
the intermediate regions at approximately 100-400 stellar radii (2"-7") away
from the star. Thus, the optical depth in the vibrational-rotational lines from
the star to the point of scattering has to be decreased. This can be
accomplished in several ways. For instance, the gas close to the star (within
approximately 2") could be in such a form that light is able to pass through,
either due to the medium being clumpy or by the matter being in radial
structures (which, further out, developes into more smooth or shell-like
structures).
