To determine the minimum conditions necessary for ignition in a small fusion target, ignition critical profiles have been calculated for a static, isobaric DT plasma filling a spherical cavity which has a specified wall temperature. The results indicate that a minimum value of the product of pressure and radius PR ≅ 4 × 106Mb·μm is required for ignition, and that the value increases as the radiation temperature decreases. The limiting value of an effective areal density derived here is smaller than previous crude estimates of a minimum ρR based on large laser fusion simulation codes, notwithstanding the fact that the plasma temperature θ is nowhere less than the wall temperature θr. Argument s are presented which suggest that the minimum PR criterion derived here should apply crudely to the case of ignition by collapse of a single strong shock. A surprising result is suggested for this dynamic case: the initial value of PR must exceed about 2 × 105 Mb·μm, compared with less than 1000 Mb·μm for DT compressed adiabatically one-thousand-fold.