Overshoots are convective air parcels that rise beyond their level of neutral buoyancy. A giga-large-eddy simulation (100-m cubic resolution) of ‘‘Hector the Convector,’’ a deep convective system that regularly forms in northern Australia, is analyzed to identify overshoots and quantify the effect of hydration of the stratosphere. In the simulation, 1507 individual overshoots were identified, and 46 of them were tracked over more than 10 min. Hydration of the stratosphere occurs through a sequence of mechanisms: overshoot penetration into the stratosphere, followed by entrainment of stratospheric air and then by efficient turbulent mixing between the air in the overshoot and the entrained warmer air, leaving the subsequent mixed air at about the maximum overshooting altitude. The time scale of these mechanisms is about 1 min. Two categories of overshoots are distinguished: those that significantly hydrate the stratosphere and those that have little direct hydration effect. The former reach higher altitudes and hence entrain and mix with air that has higher potential temperatures. The resulting mixed air has higher temperatures and higher saturation mixing ratios. Therefore, a greater amount of the hydrometeors carried by the original overshoot sublimates to form a persistent vapor-enriched layer. This makes the maximum overshooting altitude the key prognostic for the parameterization of deep convection to represent the correct overshoot transport. One common convection parameterization is tested, and the results suggest that the overshoot downward acceleration due to negative buoyancy is too large relative to that predicted by the numerical simulations and needs to be reduced.