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Monthly evapotranspiration (ET) rates for 1979-2015 were estimated by the latest, calibration-free version of the complementary relationship (CR) of evaporation over the conterminous United States. The results were compared to similar estimates of three land surface models (Noah, VIC, Mosaic), two reanalysis products (National Centers of Environmental Protection Reanalysis II, ERA-Interim), two remote-sensing-based (Global Land Evaporation Amsterdam Model, Penman-Monteith-Leuning) algorithms, and the spatially upscaled eddy-covariance ET measurements of FLUXNET-MTE. Model validations were performed via simplified water-balance derived ET rates employing Parameter-Elevation Regressions on Independent Slopes Model precipitation, United States Geological Survey two- and six-digit Hydrologic Unit Code (HUC2 and HUC6) discharge, and terrestrial water storage anomalies from Gravity Recovery and Climate Experiment, the latter for 2003-2015. The CR outperforms all other multiyear mean annual HUC2-averaged ET estimates with root-mean-square error = 51 mm/year, R = 0.98, relative bias of -1%, and Nash-Sutcliffe efficiency = 0.94, respectively. Inclusion of the Gravity Recovery and Climate Experiment data into the annual water balances for the shorter 2003-2015 period does not have much effect on model performance. Similarly, the CR outperforms all other models for the linear trend of the annual ET rates over the HUC2 basins. Over the significantly smaller HUC6 basins where the water-balance validation is more uncertain, the CR still outperforms all other models except FLUXNET-MTE, which has the advantage of possible local ET measurements, a benefit that clearly diminishes at the HUC2 scale. As the employed CR is calibration-free and requires only very few meteorological inputs, yet it yields superior ET performance at the regional scale, it may serve as a diagnostic and benchmarking tool for more complex and data intensive models of terrestrial evapotranspiration rates.