Frank et al. [1986a,b> proposed the possibility of large numbers of small comets impacting the Earth. Using the parameters for the small comets suggested by Frank and Sigwarth [1993>, we find that, over the lifetime of the solar system, such small comets would deliver far more Ar, Kr, and Xe to the atmospheres of Earth and Mars than those atmospheres presently contain if, as Frank and Sigwarth [1993> assumed, the small comets formed in very cold regions far from the Sun. Comets can be greatly depleted in noble gases if they form relatively close to the Sun (for example, near Jupiter), but this source region is inconsistent with other features of the proposed model. Alternatively, if the comets did form in very cold regions far from the Sun, the current flux would have to be at least a factor of 30,000 higher than the long-term average. ¿ 1997 American Geophysical Union