Summary: The notion of idempotent modification of an algebra was introduced by J. Ježek [Czech. Math. J. 54, No. 1, 229–231 (2004; Zbl 1048.08005)]. He proved that the idempotent modification of a group is subdirectly irreducible. For an MV-algebra \(\mathcal A\) we denote by \(\mathcal A'\), \(A\) and \(\ell (\mathcal A)\) the idempotent modification, the underlying set and the underlying lattice of \(\mathcal A\), respectively. In the present paper we prove that if \(\mathcal A\) is semisimple and \(\ell (\mathcal A)\) is a chain, then \(\mathcal A'\) is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.