The comet-tail (A (2)PI(i)-X (2)SIGMA+) system of the molecular ion (CO)-C-12-O-16+, excited in the cathode glow of a hollow-cathode discharge tube of special design, was photographed in the spectral region 3400-8500 angstrom. Of the 17 observed bands with upsilon' = 0-8 and upsilon" = 0-4, the rotational structure of 12 bands with upsilon' = 0-4 and 6 and upsilon" = 0-4 was analyzed. An effective Hamiltonian was used to obtain the molecular constants of the individual bands from their wavenumber data and the constants for the A and X states were then determined by merging the molecular constants thus obtained by the method of correlated least-squares fit. Recent experimental data of (CO)-C-12-O-16+ available for the first negative (B (2)SIGMA+-X (2)SIGMA+) and the Baldet-Johnson (B (2)SIGMA+-A (2)PI(i)) systems and for the infrared spectrum involving upsilon = 0 and 1, and the microwave spectra involving upsilon = 0, 1, and 2, of its ground state X, were reanalyzed using this effective Hamiltonian. Finally a precise set of molecular constants for the X, A, and B states of (CO)-C-12-O-16+ is determined by the procedures referred to above. The astrophysical importance of the spectra of CO+ is also briefly outlined.