The authors consider associative algebras with involution. Denote by \(*\) the fixed involution of an associative algebra \(A\) over an algebraically closed field \(\mathbb{F}\) of characteristic zero and denote by \({\mathfrak u}^*(A)\) the vector space of skew-symmetric elements of \(A\) (i.e. \({\mathfrak u}^*(A)=\{a\in A\mid a^*=-a\}\)). Then \({\mathfrak u}^*(A)\) is a Lie algebra with the usual operation of bracket multiplication. Consider the Lie algebra \({\mathfrak{su}}^*(A)=[{\mathfrak u}^*(A),{\mathfrak u}^*(A)]\). A finite-dimensional perfect Lie algebra \(L\) over \(\mathbb{F}\) is called quasiclassical if \(L\cong{\mathfrak{su}}^*(A)\). Denote by \(V\) a finite-dimensional self-dual module of \(L\) and denote by \(W\) any nontrivial composition factor of \(V\). \(V\) is called \(*\)-plain if the projection of \(L\) in \({\mathfrak{gl}}(W)\) coincides with one of the classical simple Lie algebras \({\mathfrak{sl}}(W)\), \({\mathfrak{so}}(W)\), or \({\mathfrak{sp}}(W)\) and any two composition factors of \(V\) with the same annihilator in \(L\) are either isomorphic or dual to each other. A \(*\)-plain module \(V\) is called strongly \(*\)-plain if in addition \(\dim(W)\geq 4\) for \({\mathfrak{sl}}(W)\), \(\dim(W)\geq 7\) for \({\mathfrak{so}}(W)\) and \(\dim(W)\geq 6\) for \({\mathfrak{sp}}(W)\). The authors derive that (i) if \(L\) is quasiclassical, then \(L\) is \(*\)-plain (i.e. has a faithful \(*\)-plain module); (ii) if \(L\) is strongly \(*\)-plain, then \(L\) is quasiclassical.