We have observed in the laboratory that nitrogen condenses initially as a transparent layer if the deposition rate is less than about 3 mu m/hr. To correlate our laboratory results with the Voyager observations of Triton and ground-based observations of Pluto, me have calculated the nitrogen deposition rates on these bodies. The maximum deposition rate for Pluto (with 40 K icy surface temperature) is calculated to be about 1.65 mu m/hr and for Triton is approximate to 1.38 mu m/hr at 38 K. This implies that nitrogen on these bodies may preferentially condense as a transparent layer. Voyager 2 observations in August 1989 revealed that Triton's northern hemisphere had an overall lower albedo than the southern hemisphere. This was surprising since at that time deposition of fresh Nz frost should have taken place over most of Triton's northern hemisphere (subsolar point was 45 degrees S). In contrast, the subliming southern cap was seen as a bright feature. Our new approach to this problem is based on the combination of the energy balance calculations and the laboratory results. We explain the darker northern hemisphere by the condensation of an initially transparent layer on a dark substrate, which might be dark organics produced by UV photolysis of CH4 ice. The bright southern cap can be a result of N-2 shattering due to the earlier passage of the cubic-hexagonal phase transition fronts. If there is a similar puzzling north/south albedo asymmetry on Pluto, as indicated by two independent sets of observations (hi. W. Buie, D. J. Tholen, and K. Horne, 1992, Icarus 97, 211-227; E. F. Young and R. P. Binzel, 1993, Icarus 102, 134-149), our results offer an explanation for it. We also infer an original grain size of N-2 ice on Triton and, possibly, on Pluto. The role of impurities is discussed. (C) 1997 Academic Press.