We explore the fundamental connections between certain approximate coupled cluster (CC) and generalized valence bond (GVB) wave functions. We show that the GVB restricted configuration interaction (GVB-RCI) wave function can be associated with a compact CC expansion in the valence space. However, careful analysis reveals that a standard CC expansion contains terms that are not contained in the GVB-RCI wave function. The offending terms violate an effective pairwise exclusion principle (PEP) that is present in the RCI expansion, but is not enforced in the CC analog. These terms do not affect the size separability of either method. Variational calculations show noticeable improvements to the CC wave function when the PEP is enforced, with the most significant improvements coming near the dissociation limit. We modify the standard CC amplitude equations by removing the PEP violating terms and demonstrate remarkably improved results for the dissociation of N-2 and the double dissociation of H2O.