The nonperturbative treatment of the pure dephasing problem studied by Osad’ko and Skinner and Hsu is reexamined. It is found that these treatments are inadequate for very low temperatures in the case of Ohmic friction. New nonperturbative methods are used to expose interesting pure dephasing behavior at very low temperatures in this case. The methods are shown to coincide with the previous theories at higher temperatures. The experimental detection of such phenomena is discussed.