In pump-probe experiments employing a free-electron laser (FEL) in combination with a synchronized optical femtosecond laser, the arrival-time jitter between the FEL pulse and the optical laser pulse often severely limits the temporal resolution that can be achieved. Here, we present a pump-probe experiment on the UV-induced dissociation of 2,6-difluoroiodobenzene (C6H3F2I) molecules performed at the FLASH FEL that takes advantage of recent upgrades of the FLASH timing and synchronization system to obtain high-quality data that are not limited by the FEL arrival-time jitter. Wediscuss in detail the necessary data analysis steps and describe the origin of the timedependent effects in the yields and kinetic energies of the fragment ions that we observe in the experiment.