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A mixed code is an error-correcting code in which different entries of the codewords can be chosen from different alphabets. In this correspondence an upper bound is given for the number of codewords in a mixed code where all the entries can come from distinct alphabets. This bound improves the sphere packing bound in several directions. The result is specialized to a simpler form in the case when only two distinct alphabets are used. Numerical results are presented to show that, in various cases, two different forms of the bound and alternative choices of a parameter may give the strongest bound.