The spin-lattice models relevant for the magnetic oxides Rb2Cu2(MoO4)(3), BaCu2V2O8, and KBa3Ca4Cu3V7O28 were determined by evaluating the relative strengths of the spin-exchange interactions between their Cu2+ ions on the basis of spin dimer analysis. Our study shows that the O-M-O bridges (M = V5+, Mo6+) between the magnetic ions Cu2+, provided by the MO4 tetrahedra, are crucial for the spin-exchange interactions and hence for deducing the spin-lattice models needed to interpret the magnetic properties of these oxides. The spin-lattice model of Rb2Cu2(MoO4)(3) is not a uniform chain but two interpenetrating spin ladders that interact weakly with geometric spin frustration. The spin-lattice model of BaCu2V2O8 is an alternating chain as expected, but the spin-exchange paths responsible for it differ from those expected. With respect to the strongest spin exchange of BaCu2V2O8, the spin exchange of KBa3Ca4Cu3V7O28 is only slightly weaker, but the strongest spin exchange of Rb2Cu2(MoO4)(3) is much weaker. This difference in the spin-exchange strengths is caused by the difference in the bridging modes of the MO4 tetrahedra leading to these spin-exchange interactions.