Nearly concentric optical cavities can be used to prepare optical fields with a very small mode volume. We implement an anaclastic design of such a cavity that significantly simplifies mode matching to the fundamental cavity mode. The cavity is shown to have diffraction-limited performance for a mode volume of approximate to 10(4)lambda(3). This is in sharp contrast with the behavior of cavities with plano-concave mirrors, where aberrations significantly decrease the coupling of the input mode to the fundamental mode of the cavity and increase the coupling to the higher-order modes. We estimate the related cavity quantum electrodynamics parameters and show that the proposed cavity design allows for strong coupling without a need for high finesse or small physical-cavity volume.