On endomorphism monoids in varieties of bands

It will be proved that every non-trivial variety ({mathbb{V}}) of bands (idempotent semigroups) contains a proper generating class of non-isomorphic bands B such that B generates ({mathbb{V}}) and any band ({Bprime}) having the same endomorphism monoid as B is isomorphic to B or to the opposite band B^op. Consequently, every sharply greater band variety has a sharply greater class of endomorphism monoids.