The influence of different types of precipitates (either Guinier-Preston zones, θ″ or θ′) on the critical resolved shear stress and strain hardening was determined by means of micropillar compression tests in an Al - 4 wt% Cu alloy. The size, shape and volume fraction of the precipitates were measured in each case. It was found that size effects were negligible for micropillars with diameter  ≥  5 µm. Micropillars with Guinier-Preston zones showed strain localization due to precipitate shearing. The best mechanical properties were obtained with either a fine dispersion of the θ″ precipitates or a coarser dispersion of θ′. Both precipitate shearing and Orowan loops were observed around the θ″ precipitates and the micropillar strength was compatible with the predictions of the Orowan model. In the case of the alloy with θ′ precipitates, the strengthening contribution associated with the transformation strain around the precipitates has to be included in the model to explain the experimental results. Finally, the micropillar compression tests in crystals with different orientations were used to calibrate a phenomenological crystal plasticity. This information was used to predict the mechanical properties of polycrystals by means of computational homogeneization.