European Shock Tube for High-Enthalpy Research (ESTHER) is a new state-of-the-art combustion-driven shock tube developed for supporting future ESA planetary exploration missions. Its high-pressure combustion driver sports a unique innovative design where a mixture of He:H2:O2 or N2:H2:O2 gases, filled to pressures up to 100 bar, is ignited by a high-power Neodymium-doped yttrium aluminum garnet (Nd:YAG) laser. The qualification of this facility driver has allowed for the detailed study of laser-ignited combustion processes at high initial pressures (in the 5–100 bar range), over a series of 100 shots carried out for different configurations and gas mixtures. The influence of the oxygen-to-hydrogen ratio, filling pressure, inert gas dilution, and ignition mode have been studied and are presented in this work. The effects of nitrogen vs helium dilution are also discussed. Filling pressure and helium/nitrogen dilutions have the strongest influence in peak pressure, acoustic oscillation, and combustion velocity. The first two increase, whereas the latter strongly decreases with the filling pressure. Nitrogen diluted shots have drastically lower compression ratios and flame velocity when compared to the helium ones. Acoustic perturbations/instabilities are also found to be stronger. This test campaign allowed the definition of a large range of stable and reproducible firing conditions in deflagration mode, yielding post-combustion pressures up to 660 bar.