The traditional way of dealing with uncertainty in population projections through "high" and "low" variants is unsatisfactory because it remains unclear what range of uncertainty these alternative paths are assumed to cover. Probabilistic approaches have not found their way into "official" population projections. This paper proposes an expert-based probabilistic approach (random scenario approach) that seems to meet important criteria for successful application to national and international projections: 1) it provides significant advantages to current practice, 2) it presents an evolution of current practice rather than a discontinuity, 3) it is scientifically sound, and 4) it is applicable to all countries. In a recent "Nature" article (Lutz et al. 1997) this method was applied to 13 world regions. This paper discusses the applicability to national projections by directly taking the alternative assumptions defined by the Austrian Statistical Office. Sensitivity analyses that resolve some methodological questions about the approach are also presented.