Cohomology of Deligne-Lusztig varieties for short-length regular elements in exceptional groups

We determine the cohomology of Deligne-Lusztig varieties associated to some short-length regular elements for split groups of type F4 and En. As a byproduct, we obtain conjectural Brauer trees for the principal Phi_{14}-block of E7 and the principal Phi_{24}-block of E8.