  In 1977, Keane and Smorodinsky showed that there exists a finitary
homomorphism from any finite-alphabet Bernoulli process to any other
finite-alphabet Bernoulli process of strictly lower entropy. In 1996, Serafin
proved the existence of a finitary homomorphism with finite expected coding
length. In this paper, we construct such a homomorphism in which the coding
length has exponential tails. Our construction is source-universal, in the
sense that it does not use any information on the source distribution other
than the alphabet size and a bound on the entropy gap between the source and
target distributions. We also indicate how our methods can be extended to prove
a source-specific version of the result for Markov chains.
