Diffractions from above-surface objects can be a major problem in the processing and interpretation of ground-penetrating radar (GPR) data. Whereas methods to reduce random and many other types of source-generated noise are available, the efficient suppression of above-surface diffractions (ASDs) continues to be challenging. We have developed a scheme for semiautomatically detecting and suppressing ASDs. Initially, an accurate representation of ASDs is obtained by (1) Stolt f-k migrating the GPR data using the air velocity to focus ASDs, (2) multichannel filtering to minimize other signals, (3) setting an amplitude threshold that targets the high-amplitude ASDs and effectively eliminates other signals, and (4) Stolt f-k demigrating the ASDs using the air velocity, and remigrating them using the ground velocity. By excluding the obliquity correction in the Stolt algorithms and avoiding intermediate amplitude scaling, we preserve the ASDs' amplitude and phase information. The final stepinvolves subtracting this image of ASDs from a standard migrated version of the original data. This scheme, which includes some important extensions to a previously proposed method, makes it possible to semiautomatically process large volumes of GPR data characterized by numerous highly clustered and overlapping ASDs. The user has control over the tradeoff between ASD suppression and undesired removal of useful signal. It achieves nearly complete removal of ASDs in synthetic data and significant suppression in field data. Once ASDs have been suppressed, their influence can be reduced further by applying relatively gentle multichannel filters. It is not possible to remove line diffractions that resemble subhorizontal reflections or retrieve subsurface signals from data saturated by ASDs, such that some blank regions may be left after applying the suppression scheme. Nevertheless, subsequent processing and interpretation of the GPR data benefit significantly from the suppression of ASDs, which otherwise would clutter the final images.