When analyzing irregularly sampled data to obtain climate signals, a typical starting point is to use spatial analysis methods to map observations onto a regular grid. Clear benefits are possible, however, from an alternative approach in which the desired signals are first estimated directly at the observing locations. The most important benefits relate to accuracy and error analysis. These principles are illustrated using the example of atmospheric tides. When properly estimated, the tides agree remarkably well with those simulated by the Goddard Earth Observing System general circulation model and, above the tropopause, are comparable to the mean meridional flow. ¿ 2000 American Geophysical Union