Simulations performed by a 3D cloud-resolving model are used to study the transport of near-surface tracers into the lowermost stratosphere via midlatitude convection. Direct transport by convection is believed to be the most likely mechanism by which short-lived chemical species can be transported from the boundary layer to the stratosphere. In the few works that have included analysis of cross-tropopause transport due to deep midlatitude convection, the tropopause is defined by a single altitude or pressure level, but the tropopause location is unclear in the highly perturbed environment directly above an active storm. Thus, to determine the irreversibility of cross-tropopause transport, ten-hour simulations are carried out to cover the growth and decay cycles of the storm. After the decay of convection, isentropes relax to quasi-flat surfaces, allowing more confident tropopause location. In this post-storm environment, tracer plumes extend as high as 1.9 km above the tropopause. At 1 km above the tropopause, the concentration of the tracer originating in the layer between 1 and 4 km has a maximum of 42% of its original concentration; the concentration of the tracer originating below 1 km has maximum of 19% of its original concentration. Increasing the altitude of the level of neutral buoyancy in model soundings is found to produce more transport into the stratosphere. Supercell storms produce more transport when compared with multicell storms.