A semigroup variety is called a variety of degree ≤ 2 if all its nilsemigroups are semigroups with zero multiplication, and a variety of degree > 2 otherwise. We completely determine all semigroup varieties of degree > 2 that are upper-modular elements of the lattice of all semigroup varieties and find quite a strong necessary condition for semigroup varieties of degree ≤ 2 to have the same property. © 2010 Springer Science+Business Media, Inc.