Optical-optical double resonance was employed to study rotational energy transfer in collisions of selected rotational/fine-structure levels of CN(A(2)Pi, nu = 3) with N-2. The CN radical was generated by 193 nm photolysis of BrCN in a slow flow of N-2 at total pressures of 0.2-1.4 Torr. Specific fine-structure Lambda-doublet levels of CN(A(2)Pi, nu = 3) were prepared by pulsed dye laser excitation on isolated lines in the CN A-X (3,0) band, while the initially excited and collisionally populated levels were observed after a short delay by laser-induced fluorescence in the B-A (3,3) band. Total removal rate constants for specified rotational/fine-structure levels involving total angular momentum J from 4.5 to 12.5 were determined. These rate constants decrease with increasing J, with no obvious dependence on the fine-structure/Lambda-doublet label. State-to-state relative rate constants were determined for several initial levels and show a strikingly strong collisional propensity to conserve the fine-structure/Lambda-doublet label. Comparison is made with the results of quantum scattering calculations based on potential energy surfaces averaged over the orientation of the N-2 molecule. Reasonable agreement is found with experimentally determined total removal rate constants. However, the computed state-to-state rate constants show a stronger propensity for fine-structure and A-doublet changing transitions. These differences between experiment and theory could be due to the neglect of the N-2 orientation and the correlation of the CN and N-2 angular motions.