The reaction of CuCl2·2H2O with three novel ditopic ligands, 2-methyl-1,4-benzeneditetrazolate (MeBDT2–), 4,4′-biphenylditetrazolate (BPDT2–), and 2,3,5,6-tetrafluoro-1,4-benzeneditriazolate (TFBDTri2–), affords the metal–organic frameworks Cu(MeBDT)(dmf) (1), Cu(BPDT)(dmf) (2), and Cu(TFBDTri)(dmf) (3), respectively. These materials feature a common network topology in which octahedral Cu2+ ions are bridged by azolate ligands and dmf molecules to form one-dimensional chains. The individual chains are connected by the organic bridging units to form diamond-shaped channels, in which the solvent molecules project into the pores. The bridging dmf molecules in 1 are readily displaced by other coordinating solvent molecules, which leads to a change in the pore dimensions according to the steric bulk of the solvent. Interestingly, attempts to exchange the analogous solvent molecules in the expanded framework 2 induced no change in the pore size, revealing the rigidity of the framework. Meanwhile, 3 exhibits modest flexibility and an improved thermal stability consistent with its chemical functionality. The marked difference in flexibility highlights the considerable impact the organic linker can have on the dynamic framework properties.