Some quantum-gravity theories allow for the violation of Lorentz invariance (LIV), predicting a dependence of a photon’s speed on its energy in vacuum. Because of this dependence, two photons of different energy emitted simultaneously from a distant astrophysical source may not arrive the same time at the Earth. The Fermi LAT and GBM collaborations have already placed tight constraints on LIV-induced dispersions using observations of GRBs 090510 and 080916C. In this work, using Fermi LAT observations of four selected bright GRBs and three different analysis techniques, we place stronger and more robust constraints. We will summarize the analysis and any underlying astrophysical assumptions, and present our preliminary results.