The previously developed active-space doubly electron-attacked (DEA) equation-of-motion (EOM) coupled-cluster (CC) method with up to fourparticle two-hole (4p-2h) excitations [Shen,j; Piecuch, P. J. Chem. Phys. 2013, 138; 194102], which utilizes the idea of applying a linear electron-attaching operator to the CC ground state an.(N-2), electron-closed-Shell system to generate ground, and excited states of the N-electron open-shell species of interest, has been extended to a considerably less:expensive model; in which both 3p-1h,and 4p-2h terms rather than 4p-2h contributions only are selected-using :active orbitals. As illustrated by the calculations involving low-ying singlet and triplet states of methylene; trimethylenemethane, cyclobutadiene, and cydopentadienyl cation and bond breaking, in F2, the proposect-DEA-EOMCC methed with the active-spade treatment of 3p-lh and 4p-2h\ excitations and its lower-level counterpart neglecting 4-2h Contributions are capable of accurately reproducing the results obtained using their considerably more expensive parent counterparts with a full treatment of 3p-1h :and full or active-space treatment of 4p-2h excitations,.