  This paper studies the mismatched decoding problem for binary-input discrete
memoryless channels. An example is provided for which an achievable rate based
on superposition coding exceeds the LM rate (Hui, 1983; Csisz\'ar-K\"orner,
1981), thus providing a counter-example to a previously reported converse
result (Balakirsky, 1995). Both numerical evaluations and theoretical results
are used in establishing this claim.
