The scan-line corrector (SLC) for the Enhanced Thematic Mapper Plus (ETM+) sensor, on board the Landsat 7 satellite, failed permanently in 2003. The consequence of the SLC failure (or SLC-off) is that about 20% of the pixels in an ETM+ image are not scanned. We aim to develop a geostatistical method that estimates the missing values. Our rationale is to collect three cloud-free images for a particular Landsat scene, taken within a few weeks of each other: the middle image is the target whose un-scanned locations we wish to estimate; the earlier and later images are used as secondary information. We visit each un-scanned location in the target image and, for each reflectance band in turn, predict the missing value with cokriging (resorting to kriging when there is not enough local secondary information to justify cokriging). For three Landsat scenes in different bio-regions of Queensland, Australia, we compared the performance of geostatistical interpolation with image compositing. Geostatistics was a generally superior estimator. In contrast to compositing, geostatistics was able to estimate accurately values at all un-scanned locations, and was able to quantify the variance associated with each prediction. SLC-off images interpolated with geostatistics were visually sensible, although changes in land-use from pixel to pixel affected adversely the accuracy of prediction. The primary disadvantage of geostatistics was its relatively slow computing speed. We recommend the geostatistical method over compositing, but, if speed takes priority over statistical rigour, a hybrid technique–whereby composites are corrected to the local means and variances of the bands in the target image, and any un-estimable locations are interpolated geostatistically–is an adequate compromise.