  Carbon monoxide (CO) is the most abundant molecule after molecular hydrogen
and is important for the chemistry in circumstellar envelopes around evolved
stars. When modelling the strength and shape of molecular lines, the size of
the CO envelope is an input parameter and influences the derived mass-loss
rates. In particular the low-J transition CO lines are sensitive to the CO
photodissociation radius. Recently, new CO photodissociation radii have been
published using different formalisms that differ considerably. One set of
calculations is based on an escape-probability formalisms that uses numerical
approximations derived in the early-eighties. The accuracy of these
approximations is investigated and it is shown that they are less accurate than
claimed. Improved formalism are derived. Nevertheless, the changes in CO
envelope size are small to moderate, less than 2\% for models with $10^{-7}<
\dot{M}< 10^{-4}$ \msolyr\ and at most 7\% for model with $\dot{M} = 10^{-8}$
\msolyr.
