Limiting molar conductances (λ0) of the Li+ and Cs+ ions in water have been determined at 0, −5, and −10 °C as a function of pressure up to 2 kbar. In the studied ranges of pressure and temperature, λ0(Li+) increases monotonically with increasing pressure and λ0(Cs+) has a maximum against pressure. The low-temperature conductances fit well an empirical equation of the critical law form over the pressure range studied; λ0=A(T/TS−1)γ. The parameter TS decreases with a rise in pressure below 1.5 kbar, but above that TS is almost constant. The Hubbard–Onsager (HO) dielectric friction theory has been critically tested against the experimental results obtained under the extreme conditions after λ0 are transformed into the drag coefficient (Δζ) subtracted by that due to Stokes’ law for perfect slip (4πηR). The observed pressure coefficient dΔζ/dP is negative for the small ion Li+ even in cooled or supercooled water as predicted by the HO theory but positive for the large ion Cs+ in contrast to the theoretical prediction. The following three kinds of anomalies in Δζ(Cs+) are revealed: Δζ<0, dΔζ/dP≳0, and dΔζ/dT≳0. The PTC mechanism proposed for explaining the found anomalies has been supported by model calculations; it turns out that the potential for the PTC process can be flat with a reasonable size of cavities.