The suitability of various implementations of inertial-electrostatic confinement (IEC) systems for use as D-T, D-D, D-3He, 3He-3He, p-11B, and p-6Li reactors has been examined, and several fundamental flaws in the concept have been discovered. Bremsstrahlung losses for all of these fuels have been calculated in a general fashion which applies not only to IEC systems but also to most other fusion schemes; these calculations indicate that bremsstrahlung losses will be prohibitively large for 3He-3He, p-11B, and p-6Li reactors and will be a considerable fraction of the fusion power for D-3He and D-D reactors. Further calculations show that it does not appear possible for the dense central region of a reactor-grade IEC device to maintain significantly non-Maxwellian ion distributions or to keep two different ion species at significantly different temperatures, in contradiction with earlier claims made about such systems. 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 be lost at rates greatly in excess of the fusion rate. Even by using one of the best electron confinement systems proposed for such devices, a polyhedral cusp magnetic field, and by making exceedingly optimistic assumptions about the performance of that confinement system, the electron losses from the machine prove to be intolerable for all fuels except perhaps DT. In order for IEC systems to be used as fusion reactors, it will be necessary to find methods to circumvent these problems.