The use of SAR interferometry is often impeded by decorrelation from thermal noise, temporal change, and baseline geometry. Power spectra of interferograms are typically the sum of a narrow‐band component combined with broad‐band noise. We describe a new adaptive filtering algorithm that dramatically lowers phase noise, improving both measurement accuracy and phase unwrapping, while demonstrating graceful degradation in regions of pure noise. The performance of the filter is demonstrated with SAR data from the ERS satellites over the Jakobshavns glacier of Greenland.