Time-resolved infrared-ultraviolet double-resonance (IRUVDR) spectroscopy is used to look for rotationally specific channels in collision-induced vibrational energy transfer between the nu-6 and nu-4 modes of D2 CO. The efficiency of such V-V transfer has been shown in previous work to be enhanced by a combination of Coriolis coupling and rotor asymmetry. IRUVDR spectra, recorded in pure D2 CO vapor with a range of delay intervals between IR pump and UV probe laser pulses, reveal (J,K(a))-dependent propensities in the resulting nu-6 --> nu-4 transfer arising from D2CO/D2CO collisions. At the same time, rotational relaxation within the rovibrational manifold (upsilon-6 = 1) initially prepared by the IR pump laser is found to be more pronounced than the growth of population in the neighboring upsilon-4 = 1 manifold, due to nu-6 --> nu-6 transfer. This trend is shown to be reversed in the case of D2CO/N2O collisions, where the effects of rotational relaxation appear to be less pronounced than those of nu-6 --> nu-4 transfer. This work, performed with spectroscopic resolution superior to that in previous investigations, has demonstrated a number of new effects, including the identification of weakly allowed t-type (DELTA-K(a) = 3) features in the IRUVDR spectra. It also provides the spectroscopic background to paper II of this series, which explores the detailed kinetics of (J,K(a))-resolved nu-6 --> nu-4 transfer in D2CO.