The production of highly charged ions in a CO2 laser-generated plasma is compared for different laser pulse-time structures. The work was performed at the CERN Laser Ion Source, which has the aim of developing a high current, high charge-state ion source for the Large Hadron Collider (LHC). When an intense laser pulse is focused onto a high-Z metal target, the ions expanding in the plasma plume are suitable for extraction from the plasma and matching into a synchrotron. For the first time, a comparison is made between free-running pulses with randomly fluctuating intensity, and mode-locked pulse trains with a reproducible structure and the same energy. Despite the lower power density with respect to the mode-locked pulse train, the free-running pulse provides higher charge states and higher yield.