  We discuss two possible ways of representing tolerances: first, as a
homomorphic image of some congruence; second, as the relational composition of
some compatible relation with its converse. The second way is independent from
the variety under consideration, while the first way is variety-dependent. The
relationships between these two kinds of representations are clarified.
  As an application, we show that any tolerance on some lattice L is the image
of some congruence on a subalgebra of L $\times$ L. This is related to recent
results by G. Cz\'edli and E. W. Kiss.
