The solar tachocline lies at the base of the solar convection zone. At this internal interface, motions from the unstable convection zone above overshoot and penetrate downward into the stiffly stable radiative zone below, driving gravity waves, mixing, and possibly pumping and storing magnetic fields. Here we study the dynamics of convective overshoot across very stiff interfaces with some properties similar to the internal boundary layer within the Sun. We use the Dedalus pseudospectral framework and study fully compressible dynamics at moderate to high Peclet number and low Mach number, probing a regime where turbulent transport is important. In this preliminary work, we find that the depth of convective overshoot is well described by a simple buoyancy equilibration model, and we consider implications for dynamics at the solar tachocline.