Context. A wealth of observations of CO in absorption in diffuse clouds has accumulated in the past decade at uv and mm-wavelengths Aims. Our aims are threefold: a) To compare the uv and mm-wave results; b) to interpret (CO)-C-13 and (CO)-C-12 abundances in terms of the physical processes which separately and jointly determine them; c) to interpret observed J = 1-0 rotational excitation and line brightness in terms of ambient gas properties. Methods. A simple phenomenological model of CO formation as the immediate descendant of quiescently-recombining HCO+ is used to study the accumulation, fractionation and rotational excitation of CO in more explicit and detailed models of H-2-bearing diffuse/H I clouds Results. The variation of N(CO) with N( H-2) is explained by quiescent recombination of a steady fraction n( HCO+)/n( H-2) = 2 x 10(-9). Observed N((CO)-C-12))/N((CO)-C-13) ratios generally do not require a special chemistry but result from competing processes and do not provide much insight into the local gas properties, especially the temperature. J = 1-0 CO line brightnesses directly represent N( CO), not N( H-2), so the CO-H-2 conversion factor varies widely; it attains typical values at N((CO)-C-12) less than or similar to 10(16) cm(-2). Models of CO rotational excitation account for the line brightnesses and CO-H-2 conversion factors but readily reproduce the observed excitation temperatures and optical depths of the rotational transitions only if excitation by H-atoms is weak - as seems to be the case for the very most recent calculations of these excitation rates. Conclusions. Mm-wave and uv results generally agree well but the former show somewhat more enhancement of C-13 in (CO)-C-13. In any case, fractionation may seriously bias C-12/C-13 ratios measured in CO and other co-spatial molecules. Complete C. CO conversion must occur over a very narrow range of AV and N( H-2) just beyond the diffuse regime. For N( H-2) < 7 x 10(19) cm(-2) the character of the chemistry changes inasmuch as CH is generally undetected while CO suffers no such break.
