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We present the optimal measurement strategy for distinguishing between three quantum states exhibiting a mirror symmetry. The three states live in a two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry, we understand that the transformation {|+>→|+>,|−>→−|−>} leaves the set of states invariant. The obtained measurement strategy minimizes the error probability. An experimental realization for polarized photons, realizable with current technology, is suggested.