Let M be a module and K a suhmodule of a module N in sigma[M]. We call K a delta-M-small submodule of N if whenever N = K + L, NIL is M-singular for any suhmodule L of N, we have N = L. Also we call N a delta-M-small module if N is a delta-M-small submodule of its M-injective hull. In this article, we consider (Z) over bar (delta M)(N) = Rej(N, DM), the reject of DM in N, where DM is the class of all delta-M-small modules. We investigate the properties of (Z) over bar (delta M) (N) and consider the torsion theory tau(delta V) in sigma[M] cogenerated by DM. We compare the tau(delta V) and the torsion theory tau(V) cogenerated by M-small modules and finally we give a characterization of GCO-modules.