  Carbon monoxide is the most abundant molecule after H$_2$ and is important
for chemistry in circumstellar envelopes around late-type stars. The size of
the envelope is important when modelling low-J transition lines and deriving
mass-loss rates from such lines. Now that ALMA is coming to full power the
extent of the CO emitting region can be measured directly for nearby asymptotic
giant branch (AGB) stars. In parallel, it has become obvious in the past few
years that the strength of the interstellar radiation field (ISRF) can have a
significant impact on the interpretation of the emission lines.
  In this paper an update and extension of the classical Mamon et al. (1988;
ApJ 328, 797) paper is presented; these authors provided the CO abundance
profile, described by two parameters, as a function of mass-loss rate and
expansion velocity. Following recent work an improved numerical method and
updated H$_2$ and CO shielding functions are used and a larger grid is
calculated that covers more parameter space, including the strength of the
ISRF.
  The effect of changing the photodissociation radius on the low-J CO line
intensities is illustrated in two cases.
