Let variety $\mathfrak U$ be given by the balanced identities of signature $\Omega$ not containing unary operations. Then, in the lattice of subvarieties of variety $\mathfrak U$, any element different from $\mathfrak U$ has an element covering it. In particular, variety $\mathfrak U$ might be the varieties of semigroups, groupoids, $n$-associatives, etc. It is also proven that, in the lattice of varieties of semigroups, there exists an element having a continuum of covering elements.