A lattice \(L\) with 0 and 1 is said to be upper semicomplemented if, for each \(x\in L\backslash\{0\}\), there exists \(y\in L\backslash\{1\}\) with \(x\vee y=1\). The author and \textit{M. V. Volkov} [Izv. Vyssh. Uchebn. Zaved., Mat. 1982, No. 11(246), 17-20 (1982; Zbl 0512.08004)] have asked whether every upper semicomplemented lattice of subvarieties of a variety of algebras is complemented. Here this question is answered in the affirmative for locally finite varieties of finite type, congruence- modular varieties, semigroup varieties, and several other partial cases. Recently, \textit{V. Diercks}, \textit{M. Erné} and \textit{J. Reinhold} [``Complements in lattices of varieties and equational theories'', Algebra Univers. (to appear)] answered this question in the affirmative in the general case.