The generation of nonoscillatory mirror waves is studied using a one-dimensional periodic hybrid electromagnetic simulation. The ion dynamics are treated exactly; the electrons are approximated as a finite pressure, massless fluid. Compression of the flux tubes in the magnetosheath causes a large pressure anisotropy, and it has been proposed that this anisotropy drives a mirror instability. The mirror waves have been identified by large amplitude fluctuations of the magnetic field, anticorrelated with pressure fluctuations. The simulations are initiated in a homogeneous high beta (beta=2.5) plasma with the ambient magnetic field at various angles to the simulation axis. It is found that ion cyclotron waves are also driven by the pressure anisotropy, in competition with the nonoscillatory mirror waves. Simulations indicate that in a pure 1H+ plasma the much faster growing ion cyclotron waves absorb the free energy in the anisotropy to the extent that mirror waves should not be observed. Analysis of the dispersion relations of mirror waves and ion cyclotron waves in the multi-component plasma indicates that 4He2+ and 16O6- ions in the solar wind should stabilize the ion cyclotron waves sufficiently that the mirror waves become the dominant instability.