Estimating the proportion of adaptive substitutions (α) is of primary importance to uncover the determinants of adaptation in comparative genomic studies. Several methods have been proposed to estimate α from patterns polymorphism and divergence in coding sequences. However, estimators of α can be biased when the underlying assumptions are not met. Here we focus on a potential source of bias, i.e., variation through time in the long term population size (N) of the considered species. We show via simulations that ancient demographic fluctuations can generate severe overestimations of α, and this irrespective of the recent population history.