According to Fermi models as applied to the Earth's bow shock energetic particles are accelerated most efficiently under radial interplanetary magnetic field (IMF) conditions. In an earlier paper (Sarris and Krimigis, 1988) we tested the Fermi mechanism for cases of radial IMF when no detectable ambient energetic particle fluxes were present. We concluded that the above mechanism could not account for the observations in the vicinity of the bow shock. In this work we extend the previous test by examining cases observed by the IMP 8 spacecraft where, in addition to the radial IMF, the following particle and field conditions were present: (1) in situ cyclotron-resonant wave activity, (2) a seed energetic particle population, and (3) small (≲25¿) &thgr;Bn at the points of connection of the spacecraft to the bow shock. Examination of data from days 67, 1979, and 303, 1980, show that despite the fact that all of the above conditions were satisfied, no ion enhancements (>50 keV) attributable to the Fermi process could be discerned. We conclude that, even with the addition of criteria much more stringent than those applied in all previously published upstream events, which provided the observational underpinning for the development of the Fermi model, the effects of the Fermi process in accelerating ions to energies greater than ~50 keV are essentially undetectable (&egr;<10-3) in the region upstream of Earth's bow shock. ¿ American Geophysical Union 1992