  The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic
combinatorics, that is often used to prove existence of combinatorial objects
satisfying certain constraints. Moser and Tardos have shown that the LLL gives
more than just pure existence results: there is an effective randomized
algorithm that can be used to find a desired object. In order to analyze this
algorithm Moser and Tardos developed the so-called entropy compression method.
It turned out that one could obtain better combinatorial results by a direct
application of the entropy compression method rather than simply appealing to
the LLL. We provide a general statement that implies both these new results and
the LLL itself.
