Copper and α-brass micropillars containing a single coherent twin boundary of controlled orientation were compressed to systematically investigate dislocation-twin boundary interactions as a function of the dislocation type and generalized stacking fault energies. For this purpose, bicrystalline micropillars in [112], [110] and [259] orientations were prepared from polycrystalline samples using focused ion beam milling in combination with custom 3D-printed sample holders. Consistent with previous findings, a vertical twin boundary neither resulted in the storage of dislocations at the interface nor in an increase of the sample strength when compressed in the [112] direction. However, the interface proved to be a strong obstacle for the non-screw dislocations promoted by the [259] orientation. In this case, dislocation storage – evidenced by large pile-ups – lead to a strong hardening of the specimens. The strengthening contribution of the interface was further affected by the stacking fault energy of the material. While this could be related to the different permeability of the interface, it is more likely the result of a change in cross-slip frequency within the sample volume.