The present invention relates to a device as well as a method for the additive manufacture of components by deposition of material 
layers by layer-by-layer joining of 
powder particles to one another and / or to an already produced pre-product or substrate, via selective interaction of the 
powder particles with a high-energy beam, wherein, for 
smoothing a surface of the component being produced running crosswise to the deposited material 
layers in between the deposition of two 
layers of the component, the complete 
edge region of the last layer that is applied and that runs along a surface of the component being produced is compacted in a direction of action that has a directional component parallel to the build-up direction of the layers, and / or at least one 
edge region (19) of a surface of the component (3′) is also compacted.