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[en] The superconducting proximity effect strongly modifies the local density of states in chaotic Josephson junctions. Recently we found that besides the well-known minigap a secondary gap appears just below the superconducting gap edge Δ in the limit of a large Thouless energy E_T_h >or similar Δ. To check the universality of this novel gap phenomenon we study the effect of nonideal contacts and show that the ''smile''-gap crucially depends on the transmission eigenvalue distribution. In a next step we use the random matrix method to investigate the ''smile''-gap. This allows us to approach the statistics of Andreev levels, going beyond the quasiclassical Greens function method. It turns out that the hard gap edge softens similar to what is already known from the minigap.