Millimeter wave and infrared spectra of the weakly bound dimer (CO)(2) have been studied in low-temperature pulsed supersonic jet expansions. Twenty-five new millimeter wave transitions have been observed and assigned, mostly in the 78-107 GHz region. Combined with previous data, they enable the relative energies of most of the known rotational levels (28 out of 31) in the ground vibrational state (upsilon (CO)=0) of the dimer to be determined with "microwave" accuracy (less than or similar to0.1 MHz). Four new subbands in the infrared spectrum have been assigned in terms of two new stacks of rotational levels in the excited vibrational state (upsilon (CO)=1), one stack with K=0 and the other with K=1. Energies for these levels have been determined with "infrared" accuracy (less than or similar to 10 MHz). These results contribute significantly to the considerable body of precise experimental information available for a system that is ripe for further theoretical investigation.