The paper under review studies generalizations of small and cosemisimple modules. The author proves (among other things) that a right module \(M\) over an associative ring \(R\) with unit \(M\) is a GCO-module, i.e. every singular simple right \(R\)-module is \(M\)-injective or \(M\)-projective, if and only if every \(M\)-small module in \(\sigma[M]\) is \(M\)-projective. Furthermore the author proves that \(M\) is a GV-module, i.e. every singular simple right \(R\)-module is \(M\)-injective, if and only if every \(M\)-small module in \(\sigma[M]\) is projective. In the last part of the paper the author points out that the same theorems are valid when exchanging the notion ``\(M\)-small'' by the following condition called ``\(\delta\)-\(M\)-small'', where a module \(N\) is called \(\delta\)-\(M\)-small if \(N+K\neq \widehat{N}\) holds for all submodules \(K\) of the injective hull \(\widehat{N}\) of \(N\) in \(\sigma[M]\) with \(\widehat{N}/K\) being \(M\)-singular.