In this paper, we empirically evaluate competing approaches for combining inflation density forecasts in terms of Kullback–Leibler divergence. In particular, we apply a similar suite of models to four different datasets and aim at identifying combination methods that perform well throughout different series and variations of the model suite. We pool individual densities using linear and logarithmic combination methods. The suite consists of linear forecasting models with moving estimation windows to account for structural change. We find that combining densities is a much better strategy than selecting a particular model ex ante. While combinations do not always perform better than the best individual model, combinations always yield accurate forecasts and, as we show analytically, provide insurance against selecting inappropriate models. Logarithmic combinations can be advantageous, in particular if symmetric densities are preferred.