For discrete memoryless sources with a single-letter fidelity criterion, we study the probability of the event that the distortion exceeds a level <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> , if for large block length the best code of given rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R > R(d)</tex> is used. Lower and upper exponential bounds are obtained, giving the asymptotically exact exponent, except possibly for a countable set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</tex> values.