We have studied the effect of counterion binding efficiency on the linear viscoelastic properties of wormlike micelles formed from hexadecyltrimethylammonium bromide (CTAB) in the presence of different nonpenetrating inorganic salts: potassium bromide (KBr), sodium nitrate (NaNO(3)), and sodium chlorate (NaClO(3)). We have varied the salt/surfactant ratio R at fixed surfactant concentration of 350 mM. Results are compared to data for the system cetylpyridinium chloride (CPyCl) and the penetrating counterion sodium salicylate (NaSal) (Oelschlaeger, C.; Schopferer, M.; Scheffold, F.; Willenbacher, N. Langmuir 2009, 25, 716-723). Mechanical high-frequency rheology and diffusing wave spectroscopy (DWS) based tracer microrheology are used to determine the shear moduli G' and G'' in the frequency range from 0.1 Hz up to 1 MHz (Willenbacher, N.; Oelschlaeger, C.; Schopferer, M.; Fischer, P.; Cardinaux, F.; Scheffold, F. Phys. Rev. Lett. 2007, 99, 068302, 1-4). This enables us to determine the plateau modulus G(0), which is related to the cross-link density or mesh size of the entanglement network, the bending stiffness kappa (also expressed as persistence length l(p) = kappa/k(B)T) corresponding to the semiflexible nature of the micelles, and the scission energy E(sciss), which is related to their contour length. The viscosity maximum shifts to higher R values, and the variation of viscosity with R is less pronounced as the binding strength decreases. The plateau modulus increases with R at low ionic strength and is constant around the viscosity maximum; the increase in G(0) at high R, which is presumably due to branching, is weak compared to the system with penetrating counterion. The scission energy E(sciss) approximately = 20 k(B)T is independent of counterion binding efficiency irrespective of R and is slightly higher compared to the system CPyCl/NaSal, indicating that branching may be significant already at the viscosity maximum in this latter case. The micellar flexibility increases with increasing binding efficiency of counterions according to the Hofmeister series. The persistence length values for systems CTAB/KBr, CTAB/NaNO(3), and CTAB/NaClO(3) are 40, 34, and 29 nm, respectively, independent of R, and are significantly higher than in the case of CPyCl/NaSal.