A fully kinetic theory of the magnetic mirror instability in high-¿ space plasmas accounting for arbitrary ion-Larmor radius effects is developed. It is shown that incorporation of ion-Larmor radius effects leads to a substantial modification of both the instability growth rate and the instability threshold. For wavelengths of the order of the ion-Larmor radius the effective elasticity of the magnetic field lines is substantially enhanced, yielding an increase in the instability threshold. We derive a compact expression for the growth rate of the fastest-growing mode in the fully kinetic limit. Furthermore, it is shown that in the presence of finite ion-Larmor radius effects a noncoplanar component of the magnetic field perturbations appears. Such a component is usually present in satellite measurements of mirror modes. The relevance of these results in understanding observations of mirror instability--generated signals in space plasmas is outlined.