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Submarine volcanic eruptions can perturb the water surface and subsequently generate localised tsunamis. Herein waves are produced in analogous laboratory experiments by injections of non-condensable expanding air into fresh water. By varying source pressures, jet durations and water depths, we obtain two key results. There exists a saturation duration above which the maximum wave height will not increase as the eruption continues. Apart from in extremely shallow or deep water depths, this saturation duration is positively correlated with the source intensity and negatively with the water depth. There also exists a critical water depth where an eruption with a given source intensity can generate the largest waves. When an eruption lasts less than the saturation duration, increasing the eruption duration will increase the critical water depth and the corresponding maximum wave height. The saturation duration and critical water depth are the primary controls on tsunami size and hazard.