This paper addresses in a systematic demographic manner the widely discussed question: To what extent can immigration compensate for low fertility in Europe? We begin with a set of 28 alternative scenarios combining seven different fertility levels with four different migration assumptions at the level of the EU-15 to 2050.  Next, we address the research question in the context of probabilistic population projections, and the new concept of conditional uncertainty distributions in population forecasting is introduced. Statistically this is done by sorting one thousand simulations into low, medium, and high groups for fertility and migration according to the average levels of paths over the simulation period. The results show a similar picture to that of the probability-free scenarios, but also indicate that for the old-age dependency ratio, the uncertainty about future mortality trends greatly adds to the ranges of the conditional uncertainty distributions.