This paper provides a derivation from first principles of the stringent symmetry and stability requirements which deep stellar nulling demands, and also includes a brief status report on recent nulling results obtained with the Jet Propulsion Laboratory's fiber-coupled rotational-shearing interferometer. To date, the deepest transient nulls obtained (at red wavelengths) are 2 X 10-6 with a laser diode source, and 1.4 X 10-5 with a single- polarization thermal white-light source filtered to provide an 18% passband. In addition, both the laser and white light nulls have been stabilized to the 10-4 level. This visible wavelength laboratory nuller thus meets essentially all of the performance goals for the planned nulling experiment on board NASA's Space Interferometer Mission, with the sole exception of dual-polarization operation.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.