After a brief review of the data augmentation (DA) algorithm, I will
introduce a simple modification that results in a new Markov chain
that remains reversible with respect to the target distribution.  We
call this modification the "sandwich algorithm" because it involves an
extra move that is sandwiched between the two conditional draws of the
DA algorithm.  General results will be presented showing that the
sandwich algorithm is at least as good as the underlying DA algorithm
in terms of both efficiency and convergence rate.