The soil and crop cover of agricultural land vary spatially in a way that is both random and autocorrelated. This enables them to be estimated and mapped from sparse sample data by kriging. These properties (primary variables) are usually related to the radiation they reflect: They are coregionalized with it. In many circumstances the primary variables can be estimated more precisely by measuring, in addition, the radiation sparsely, using a ground-based radiometer and combining the two by cokriging. The coregionalization must be formalized in a coherent set of variograms, one for the primary variable, one for each variable derived from the radiometry, and the cross variograms between all pairs of variables involved in the estimation. Given this set, it is possible to determine estimation variances for any configuration of sampling and to design an optimal scheme that will achieve a desired precision for least effort. The formulae for cokriging are presented, as are the conditions for a coherent model of the coregionalization, and the article shows how these can be used to design sampling schemes that combine survey of the primary variables and radiation to best advantage. Three examples from intensive agriculture in Britain illustrate the technique. In one example where the aim was to estimate and map the cover of clover in pasture, cokriging using measured radiation was nine times as efficient as kriging the cover alone.