Ve calculate the overabundances of rare neutron-rich species produced when seed nuclei between silicon and nickel are exposed to small neutron irradiations in order to ascertain whether those species may owe their natural abundances to such a cause, Particular attention is given to 54Cr and 58Fe, two relatively prominent neutron-rich species that have been bypassed by calculation of explosive nucleosynthesis. Although it is possible that 58Fe is due to weak s-processes, it seems unlikely that 54Cr can be produced along with it because its calculated overabundance is so much less than that of 55Fe. Uncertainties in key neutron-capture cross-sections do not allow this statement to be made unequivocally, however. If 58Fe is due to weak s-process irradiations, moreover, it seems that certain lighter species syn thesixed satisfactorily in explosive oxygen and silicon burning, such as Cl and 41K, must also be synthesixed in the s-process. e regard this as unlikely and therefore doubt that the s-process has played a major role in the synthesis of these nuclei. Accordingly, the origins of 54Cr and 58Fe remain somewhat of a mystery. The suggestion of Amiet and Zek that the rtrocess nuclei are the heavy seeds for the s-process is ruled out.