For fast-pulse laser-crystallized thin-film Si on non-crystalline substrates, the average grain size exhibits a peak as a function excimer laser energy density at a characteristic laserfluence FM. The average grain size increases with increasing laser fluence and can reach a maximum value on the order of 10 pm or about 100 times the film thickness. The grain size then decreases with further increases in fluence. This peak in grain size is accompanied by a similar peak in the Hall electron mobility and x-ray scattering intensity. Our experiments have investigated as-deposited and ion-implanted samples, using a double-scan laser crystallization process. Devices have also been fabricated and studied. The results are consistent with the increase in grain size occurring because of the destruction of nucleation sites with increasing laser fluence (i.e., increased heating and complete Melting). But substrate damage occurs in the vicinity of FM, creating nucleation sites which give rise to small grain sizes in the solidified film. The disruption of the interface causes substantial current leakage through the dielectric of bottom-gate transistors, implying that devices should be laser fabricated below Fm.