  We derive a sphere-packing error exponent for coded transmission over
discrete memoryless channels with a fixed decoding metric. By studying the
error probability of the code over an auxiliary channel, we find a lower bound
to the probability of error of mismatched decoding. The bound is shown to decay
exponentially for coding rates smaller than a new upper bound to the mismatch
capacity which is established in this paper. For rates higher than the new
upper bound, the error probability is shown to be bounded away from zero. The
new upper bound is shown to improve over previous upper bounds to the mismatch
capacity.
