  We study local-search satisfiability solvers for propositional logic extended
with cardinality atoms, that is, expressions that provide explicit ways to
model constraints on cardinalities of sets. Adding cardinality atoms to the
language of propositional logic facilitates modeling search problems and often
results in concise encodings. We propose two ``native'' local-search solvers
for theories in the extended language. We also describe techniques to reduce
the problem to standard propositional satisfiability and allow us to use
off-the-shelf SAT solvers. We study these methods experimentally. Our general
finding is that native solvers designed specifically for the extended language
perform better than indirect methods relying on SAT solvers.
