Several previous studies have attempted to remove the effects of explosive volcanic eruptions and El Niño-Southern Oscillation (ENSO) variability from time series of globally averaged surface and tropospheric temperatures. Such work has largely ignored the nonzero correlation between volcanic signals and ENSO. Here we account for this collinearity using an iterative procedure. We remove estimated volcano and ENSO signals from the observed global mean temperature data, and then calculate trends over 1979-1999 in the residuals. Residual trends are sensitive to the choice of index used for removing ENSO effects and to uncertainties in key volcanic parameters. Despite these sensitivities, residual surface and lower tropospheric (2LT) trends are almost always larger than trends in the raw observational data. After removal of volcano and ENSO effects, the differential warming between the surface and lower troposphere is generally reduced. These results suggest that the net effect of volcanoes and ENSO over 1979-1999 was to reduce globally averaged surface and tropospheric temperatures and cool the troposphere by more than the surface. ENSO and incomplete volcanic forcing effects can hamper reliable assessment of the true correspondence between modeled and observed trends. In the second part of our study, we remove these effects from model data and compare simulated and observed residual trends. Residual temperature trends are not significantly different at the surface. In the lower troposphere the statistical significance of trend differences depends on the experiment considered, the choice of ENSO index, and the volcanic signal decay time. The simulated difference between surface and tropospheric warming rates is significantly smaller than observed in 51 out of 54 cases considered. We also examine multiple realizations of model experiments with relatively complete estimates of natural and anthropogenic forcing. ENSO and volcanic effects are not removed from these integrations. As in the case of residual trends, model and observed raw trends are in good agreement at the surface but differ significantly in terms of the trend differential between the surface and lower troposphere. Observed and simulated lower tropospheric trends are not significantly different in 17 out of 24 cases. Our study highlights the large uncertainties inherent in removing volcano and ENSO effects from atmospheric temperature data. It shows that statistical removal of these effects improves the correspondence between modeled and observed temperature trends over the satellite era. Accounting for volcanoes and ENSO cannot fully explain the observed warming of the surface relative to the lower troposphere, or why this differential warming is not reproduced in the model simulations considered here.