Let be a nontrivial bounded lattice (or
a complemented lattice, etc.). Then is a tight lattice if every proper tolerance of satisfies

Tight lattices play an important role in the study of congruence lattices on finite algebras. One can show that a finite lattice is tight if and only if it is -simple and every strictly increasing meet endomorphism of
is constant. One can also show that
a finite lattice
is tight if and only if its only connected tolerance is the all relation, .

Grätzer, G. General Lattice Theory, 2nd ed. Boston, MA: Birkhäuser, 1998.Hobby,
D. and McKenzie, R. The
Structure of Finite Algebras. Providence, RI: Amer. Math. Soc., 1988.Insall,
M. "Some Finiteness Conditions in Lattices Using Nonstandard Proof Methods."
J. Austral. Math. Soc.53, 266-280, 1992.