The abundances and spectra of 1-10 MeV per nucleon protons, He-3, He-4, C, O, and Fe have been exmained during solar quiet periods from 1978 to 1987 in an effort to investigate the recent suggestion by Wenzel et al. (1990) that the ions may be of solar origin. It is found that the intensities of the ions, other than O, fall by an order of magnitude between solar maximum and solar minimum, and that the greater than 1 MeV per nucleon ions exhibit weak streaming away from the sun. More significantly, the quiet-time ions during solar maximum have He-3-rich and Fe-rich abundances which are established characteristics of small impulsive solar flares. Thus, it is suggested that small unresolved impulsive flares make a substantial contribution to the 'quiet-time' fluxes. He-4 from these flares may also contribute strongly to the ion spectra that were reported for the 35-1600 keV energy range by Wenzel et al.