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, .