The G4-SP and G4(MP2)-SP procedures are introduced, as alternatives to G4 and G4(MP2), to overcome shortcomings associated with the treatment of spin polarization (SP) in large open-shell systems. The new methods employ a converging SP term, to replace the diverging A′ treatment used in the G4 and G4(MP2) formulations. The G4-SP and G4(MP2)-SP procedures have mean absolute deviations (MADs) from experimental energies of 3.49 and 4.37 kJ mol -1, respectively, for the G3/05 test set, which are comparable to the MAD values for G4 and G4(MP2) but eliminate the problem of a diverging A′ term. For energies involving larger radicals, G4(MP2)-SP performs better than standard G4(MP2). Alternative methods, including G4-5H, G4(MP2)-5H, G4-sc, and G4(MP2)-sc, are also introduced to avoid the problem of an indefinitely increasing SP correction in standard G4 or G4(MP2) for reactions involving larger open-shell systems.