We evaluate in detail the stability requirements for a band-limited coronagraph with an inner working angle as small as 2 λ/D coupled to an off-axis, 3.8-m diameter telescope. We have updated our methodologies since presenting a stability error budget for the Terrestrial Planet Finder Coronagraph mission that worked at 4 λ/D and employed an 8th-order mask to reduce aberration sensitivities. In the previous work, we determined the tolerances relative to the total light leaking through the coronagraph. Now, we separate the light into a radial component, which is readily separable from a planet signal, and an azimuthal component, which is easily confused with a planet signal. In the current study, throughput considerations require a 4th-order coronagraph. This, combined with the more aggressive working angle, places extraordinarily tight requirements on wavefront stability and opto-mechanical stability. We find that the requirements are driven mainly by coma that leaks around the coronagraph mask and mimics the localized signal of a planet, and pointing errors that scatter light into the background, decreasing SNR. We also show how the requirements would be relaxed if a low-order aberration detection system could be employed.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.