We have searched for the hypothetical small comets proposed by Frank et al. [1986a, b> and Frank and Sigwarth [1993> using the world's most powerful radar in terms of gain-aperture product. The Naval Space Surveillance System can detect most space objects in low Earth orbit with radar cross sections (RCSs) of 0.1 m2 or larger; at higher altitudes of the order of 10,000--20,000 km the radar can detect objects with RCSs of 1 m2. We carried out detailed first-principle calculations of the RCS of spherical comct using the properties proposed by Frank and Sigwarth [1993>. We find that 8--12 m diameter comets have an average cross section of 0.4 m2 at the radar frequency (217 MHz), with peaks reaching 1 m2. Therefore the Naval radar system has sufficient sensitivity to detect many small comets, especially as they approach low Earth orbit. We estimate that at least 800--5000 small comets should have been detected by the radar during the 37 day search period during fall 1997. None of the more than 12,000 unidentified detections can be explained by small comets. The lack of detection of small comets by the radar can be explained only if small comets have RCSs <0.1% of their assumed physical size (which is unrealistic, given that human technology can match this value only by tailoring a design for a specific radar) or if their impact rate with Earth is some 4 orders of magnitude less than proposed by Frank et al. [1986a> and Frank and Sigwarth [1993>. ¿ 1999 American Geophysical Union