Results are presented of cross-sectional transmission-electron microscopy and optical reflectivity investigations into the excimer-laser annealing of a-Si films. It is found that, in the initial stages of the excimer pulse, explosive crystallization leads to small, columnar and defect-rich grains. We discuss the evolution of this microstructure as the laser energy is slowly increased up to and beyond the super-lateral growth regime. We argue that melting along grain boundaries and defects is a crucial step in obtaining large single-crystalline grains.