Spin unrestriction is typically defined as a free variation of the molecular orbitals of different spins in order to lower the molecular energy. When applied to approximate active space electron correlation methods, such as generalized valence bond coupled cluster (GVB-CC) models, this approach often leads to Undesirable artifacts. We therefore present an alternative Unrestricted in active pairs (UAP) procedure for spin polarization in GVB-CC methods, which resembles the corresponding orbitals of unrestricted Hartree-Fock theory. The UAP procedure permits spin polarization only within the two orbital subspaces describing each electron pair (consisting of one nominally occupied and one virtual orbital). This great reduction to just a linear number of degrees of freedom associated with spin polarization eliminates many of the undesirable artifacts associated with unconstrained spin unrestriction. The UAP procedure is tested on a variety of potential curves for bond breaking and the properties of small radicals its well as larger polyenyl radicals, allyl, pentadienyl, and heptatrienyl.