Arrangements for combination and fast-axis alignment of fast-axes of diode-laser beams are disclosed. Alignment arrangements include providing each diode-laser with a corresponding alignable fast-axis collimating lens, providing individually alignable mirrors for steering an re-orienting beams from each diode-laser, and providing single diode-laser slab-modules in which the diode-laser beams can be pre-aligned to a common propagation-axis direction, and in which edges and surfaces of the slabs can be used to align the fast and slow-axes of the beams. Beam combination methods include combination by dichroic elements, polarization-sensitive elements, and optical fiber bundles.