The support is a geostatistical term used to describe the size, geometry and orientation of the space on which an observation is defined. In remote sensing, the size of support is equivalent to the spatial resolution. The relation of size of support with the precision of estimating the mean of several properties is evaluated by kriging. The authors chose three examples; estimating the dry biomass of pasture on May 6, 1988, and estimating the percentage cover of clover in the pasture and its NDVI (measured using a ground-based radiometer) on Aug. 6, 1988. The modelled experimental variograms of these properties were deregularized to estimate the punctual variograms and these functions regularized to new sizes of support. The regularized variograms were then used to estimate the kriging variances attainable by sampling on a square grid. The kriging variances were plotted against grid spacing for each new size of support and the optimal sampling strategy read from the graph. In each case, there were several optimal sampling strategies, and the final choice depended on the cost of measurement. In some cases increasing the size of support was more efficient than increasing the sampling intensity.