Let \(R\) be an algebra, \(\Gamma(R)\) be its centroid and \(A(R):=\{\phi\in\Gamma(R):\phi R\subseteq \text{Ann}(R)\}\). \(\Gamma(R)\) is called small if, for some decomposition of \(R\) into a finite direct sum of directly indecomposable algebras \(R_i\), the factors \(\Gamma(R_i)/A(R_i)\) are fields. Generalizing the result of \textit{D. J. Melville} [Commun. Algebra 20, 3649--3682 (1992; Zbl 0954.17502)], the author proves the following theorem: If \(U\) is a reductive finite-dimensional Lie algebra of characteristic \(0\) and \(R\) is its subalgebra, which is invariant under an adjoint action of some Cartan subalgebra of \(U\), then \(\Gamma(R)\) is small. Moreover, he proves that if \(R\) is a finite-dimensional algebra of characteristic \(0\) and \(t\) is its effective derivation then \(\Gamma(R)\) is small.