We have investigated thermal and suprathermal protons (from ~13 keV to ~1 MeV) and alpha particles (from ~30 keV/Q to 130 keV/Q) in the quasi-stable plasma sheet near local midnight at geocentric distances of ~12--20 RE. The data, obtained during five different plasma sheet penetrations with the Max-Planck-Institut/University of Maryland sensor system on ISEE 1, represent the first measurements of plasma sheet ion composition in this energy range. Below ~16 keV the proton spectra can be represented by a Maxwellian distribution. Above ~16 keV we find a suprathermal tail which cannot be represented by a single power law. In some cases the suprathermal population consists of two distinct components: a low-energy component falling off sharply at ~100 keV and a high-energy component extending up to ~1 MeV. The high-energy component often decays with time during expansion of the plasma sheet. Alpha particle to proton ratios average ~3% and are observed to be constant at either equal energy per nucleon or energy per charge.