Infrared ultraviolet double resonance (IRUVDR) experiments have been performed to investigate the rotational specificity of the vibrational-vibrational (V-V) exchange process, NO(X (2)Pi(1/2),v=3,J(i))+NO(v=0)--> NO(X (2)Pi(1/2),v=2,J(f))+NO(v=1), for which the vibrational energy discrepancy corresponds to 55.9 cm(-1). Radiation from an optical parametric oscillator was used to excite NO molecules into a specific rotational level (J(i)) in the X (2)Pi, Omega=1/2, v=3 state. Laser-induced fluorescence (LIF) spectra of the (0,2) band of the A (2)Sigma(+)-X (2)Pi(1/2) system were then recorded at delays corresponding to a fraction of a collision. From the relative line intensities, rate coefficients were determined for transfer of the excited NO molecule from the level X (2)Pi(1/2), v=3, J(i) to different final rotational levels (J(f)) in the X (2)Pi(1/2), v=2 state. Results are reported for J(i)=3.5, 4.5, 7.5, 10.5, and 15.5. The data show a significant, though not strong, propensity for J to decrease by one; i.e., for Delta J=J(f)-J(i)=-1, especially for the higher J(i) levels. This result is interpreted as arising from a combination of (a) the tendency to minimize the energy that has to be accommodated in the relative translation of the collision partners, and (b) the favoring of Delta J=+/- 1 changes when V-V intermolecular exchange occurs under the influence of dipole-dipole interactions.