In principle the dynamic atmosphere correction (DAC) for altimetry should have no tidal signals, as tide corrections are expected to be most accurately determined by ocean tide models. Tidal SSH oscillations include both gravitational tides, driven by the tidal potential, and radiational tides, driven predominantly by loading by atmospheric tides, and our current ocean tide models include both components. Thus, the OSTST conventions require removing atmospheric tides from the DAC forcing, and the LEGOS/CNES team does this by subtracting a climatological air-tide model from ECMWF air pressures. However, the removal is only partially successful, owing primarily to errors in ECMWF tides. It turns out that ECMWF tides have small trends which, as we move away from the period when the climatological model was developed, cause more and more tidal signal to leak into the DAC forcing, and hence into the DAC correction. Although secular trends in the real S2 air tide might be expected, owing to secular trends in stratospheric ozone, comparisons against "ground truth" barometric pressures suggest that the ECMWF trends are spurious. In addition, lunar air tides have been left unfiltered in DAC forcing, likely because their amplitudes are everywhere less than 10 Pa (with an equilibrium ocean response less than 1 mm). But the ocean responds to M2 in near-resonance, so the M2 radiational tide can reach 5 mm and should therefore be removed from DAC forcing. The ECMWF M2, like S2, has spurious secular trends; these trends are most likely induced by changes in ECMWF data assimilation over time (cf. Schindelegger and Dobslaw, 2016). Finally, the ECMWF pressures appear to have some curious nonlinear tide-like signals, such as at the frequency of MS4, for which I can find no evidence in barometric measurements. Because tidal leakage in the DAC correction had been anticipated, to some extent, the high-frequency DAC was not used during the development of most GOT and TPXO models, making these models somewhat inconsistent with the current DAC correction for altimeter users, but making them more accurate for other applications (e.g., GRACE). It is recommended that the current ECMWF filtering procedures be amended to remove more completely the atmospheric tide signals, be they real or spurious.