The suitability of various implementations of inertial-electrostatic confinement (IEC) systems'for use as D-T, D-D, D-3 He, p-l 1 B, and p-6 Li reactors is examined; these IEC designs create a deep electrostatic potential well within the plasma in order to confine and accelerate ions, and they typically use magnetic fields or electrostatic grids to confine electrons. It is shown that while an IEC reactor would have the advantages of high power densities and relatively simple engineering design when compared with other fusion schemes, it suffers from several flaws. Foremost among these problems is that on the basis of velocity-space diffusion calculations, it does not appear to be possible for the dense central region of a reactor-grade device to maintain significantly non-Maxwellian ion distributions or to keep two different ion species at significantly different temperatures; this discovery contradicts earlier claims of the particular suitability of IEC systems for advanced fuels. Since the ions form a Maxwellian distribution with a mean energy not very much smaller than the electrostatic well depth, ions in the energetic tail of the distribution will likely be lost at rates greatly in excess of the fusion rate. Furthermore, even optimistic assumptions about the performance of the surrounding polyhedral cusp magnetic field lead to the conclusion that the electron losses from the machine will be intolerable for all fuels except DT. If electrostatic grids are used instead of magnetic cusps, the particle losses should be even worse. Finally, because the Maxwellian ion distributions are not fundamentally different than those in other fusion schemes, bremsstrahlung losses will be similar; in particular, the ratio of bremsstrahlung power to fusion power will at best be -1.7 for p-11 B and -5.4 for p-6 Li, demonstrating that IEC cannot utilize proton-based fuels in a practical manner. In order for IEC systems to be used as fusion reactors, it will be necessary to find methods to circumvent these problems.