The internal viscosity (IV) polymer chain model, which features an interbead connector functioning as a Hookean spring and a dashpot in parallel, is examined for the case of dumbbells(N=2)in the limit of very high IV. When the IV parameter Φ becomes very large, the moments of the configurational diffusion equation become identical to those of the rigid rod, thus establishing equivalence of rheological predictions for these two models. Next, an approximate linearization (preaveraging) technique for computing bead deformational and rotational velocities—previously found to give useful results in the limitΦ→0—is examined also in the limitΦ→∞.Predictions for non‐Newtonian viscosity and first normal stress coefficient are made using both the exact and approximate methods. Major differences are found, with the approximate method leading to an unrealistic (Newtonian) viscosity and vanishing normal stress, thus casting doubt on earlier results obtained with this method for high‐Nchains with large Φ. For the exact method, replacement of monodisperse dumbbells by a Gaussian distribution of dumbbell lengths has no effect on the low‐shear viscosity, but increases the low‐shear normal stress by a factor of 5/3; at high shear the two types of distributions give very similar results.