Frank et al. [1986b] and Frank and Sigwarth [1993] hypothesized the intense bombardment of the terrestrial atmosphere by small comets. Their model requires that the Moon is impacted by small comets (10(7)-10(8) g) at a rate of almost one per minute. We calculate that an object of this mass, even with an exceedingly low density and relatively low velocity, will nevertheless produce a crater at least 50 m in diameter. These craters will excavate immature lunar soil and produce a very bright spot with a diameter df at least 150 m. If low-density comets exist that might not create deep craters [O'Keefe and Ahrens, 1982], they will nevertheless disturb the regolith sufficiently to create detectable bright spots. If the small-comet hypothesis is correct then the near-global lunar imaging returned by Clementine in 1994 should reveal similar to 10(7) bright spots in locations where craters are not present in images acquired in the 1960's and early 1970's. We find no new bright limit to the current cratering rate by small comets is 33/yr, similar to 10(4) below that expected if the small-comet hypothesis were valid.