New extensive millimeter-wave measurements of the (CO)-C-12-O-16 dimer have been made, and more than 300 new spectral transitions have been observed in the frequency range 81-135 GHz. A joint analysis of these and previous millimeter-wave data yielded the precise location of 33 new energy levels of A(+) symmetry and 20 levels of A(-) symmetry. These energy levels are located at 8-18 cm(-1) above the zero-point level. Some of them belong to already known stacks, and others make up 9 new stacks of the dimer. Newly determined stacks have K = 0, 1, and, for the first time, 2, where K is the projection of the total angular momentum on the intermolecular axis. The energy levels from accompanying rovibrational calculations with the use of a recently developed hybrid CCSD(T)/DFT-SAPT potential are in very good agreement with experiment. Analysis of the calculated wave functions revealed that two new stacks of A(+) symmetry with K = 2 correspond to overall rotation of the dimer while the other newly observed stacks belong to the geared bend overtone modes. The ground vibrational states of the two "isomers" found are more or less localized at the two minima in the potential surface, whereas all the geared bend excited states show a considerable amount of delocalization.