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A source matching approach is presented to the problem of finding minimax cedes for classes of memoryless sources. The approach leads to a channel capacity problem so that Blahut's algorithm can be used to find approximations to the minimax code. Closed form solutions are presented for the class of monotonic sources and for a class of Bernoulli-like sources. For extensions of finite alphabet memoryless sources, a modified Lynch-Davisson code has performance close to that of the minimax code. The exact solution to the source matching problem and the resulting codes are presented for the extensions of binary codes up to blocklength 31.