Results are presented from studies of microinstabilities in a model mirror plasma. The model has a Gaussian density distribution of ions and electrons along a varying magnetic field, and a radial density gradient perpendicular to this field. Particles are contained self-consistently by a fictitious confining potential modelling mirror confinement. The ion velocity-space distribution is the finite-plasma equivalent of a Guest-Dory loss-cone distribution, and the electron distribution allows for finite-temperature effects, including Landau damping. Resonant and non-resonant loss-cone instabilities are discussed. It is found that resonant instabilities are stabilized when the plasma length is less than a critical length which is dependent upon electron temperature, but modes corresponding to flute modes in homogeneous plasmas (Dory-Guest-Harris and drift-cone) are found to remain unstable at all plasma lengths.