Data from the Pioneer Venus orbiter magnetometer, plasma wave detector and Langmuir probe are used to investigate the scale thickness and controlling factors associated with the current sheet at the Venus ionopause, the boundary between the ionosphere and the solar wind. The current sheet is found to have two principal scale sizes: (1) a few ion gyroradii when the external compressed solar wind field is less than 80 mT and the ionopause altitude is above ~300 km; (2) several tens of ion gyroradii when high external fields occur and ionopause altitudes are below ~300 km. The current sheet thickness may be significantly affected by collisional diffusion at low altitudes, and wave turbulence may also play a role in controlling thickness. The high-altitude boundaries are consistent with the expected thickness of the thinnest charge-neutral, collisionless current sheet.