Global three-dimensional (3-D) model calculations have been used to inversely determine OH concentrations from 1,1,1-trichloroethane (methyl chloroform or CH3CCl3) measurements at the Atmospheric Lifetime Experiment (ALE)/Global Atmospheric Gases Experiment (GAGE)/Advanced GAGE (AGAGE) measurement stations. Annual global and biannual hemispheric estimates of OH show large fluctuations. With the aid of pseudo data, it is shown that these estimates are sensitive to simplifying assumptions in the model that is used for the inversion. The use of climatological transport and errors in the emissions cause spurious fluctuations in the retrieved OH levels. If only the slow OH variations are considered, an OH increase of about 12% is calculated in the 1978--1990 period, which is followed by a slightly larger decline in the 1991--2000 period. The N/S interhemispheric ratio is optimized to a value of about 0.98. Model calculations indicate that because of a rapidly decreasing CH3CCl3 burden in the 1990s, the stratospheric sink has become less important. Moreover, owing to the changed CH3CCl3 distribution, interhemispheric transport of CH3CCl3 has ceased in recent years. These effects lead to systematic differences with results obtained with highly parameterized models with very low resolution. The large OH anomaly that is inferred around 1990 vanishes if CH3CCl3 emissions of about 65 Gg were delayed from the early to the late 1990s.