We present the results of a series of high-resolution, three-dimensional numerical experiments that investigate the nature of turbulent compressible convective motions extending from a convection zone into a stable layer below. In such convection, converging flows in the near-surface cellular convecting network create strong downflowing plumes that can traverse the multiple scale heights of the convection zone. Such structures can continue their downward motions beyond the convecting region, piercing the stable layer, where they are decelerated by buoyancy braking. If these motions mix entropy to an adiabatic state below the convection zone, the process is known as penetration; otherwise it is termed overshooting. We find that in threedimensional turbulent compressible convection at the parameters studied, motions generally overshoot a significant fraction of the local pressure scale height but do not establish an adiabatic penetrative region, even at