Recent observations in Earth's magnetosheath have delineated several different kinds of magnetic fluctuation spectra below the proton cyclotron frequency. This paper provides a theoretical interpretation for some of these observations, describing solutions of the linear Vlasov dispersion equation for fully electromagnetic instabilities for particle distributions which model those observed in the magnetosheath. The model assumes a high-&bgr;, homogeneous plasma with bi-Maxwellian, anisotropic (T⊥p>T∥p) protons; a similarly anisotropic, tenuous, doubly ionized helium component; and isotropic cool electrons. The model also assumes a uniform magnetic field and no relative average drifts among the components. This model yields three growing modes: the proton cyclotron anisotropy, the helium cyclotron anisotropy, and the mirror instabilities. The regimes in &bgr;p versus T⊥p/T∥p space which correspond to maximum growth rates of the mirror and proton cyclotron anisotropy instabilities are computed, including helium densities appropriate for the magnetosheath; the results show very good agreement with the observations of mirror-like and proton-cyclotron-like events. This agreement with observations implies that the transition between cyclotron and mirror fluctuation dominance is consistent with linear theory. ¿ American Geophysical Union 1993