Low soil fertility is a major constraint for increasing millet production on the acid sandy soils of the West African Sahel. On these soils, all three macronutrients- nitrogen (N), phosphate (P) and potassium (K), may be expected to limit crop yields. The important question is therefore: which of them is the most critical and would, if applied in small amounts, increase yields significantly? This paper addresses this question with an empirical approach, thus avoiding the commonly observed difficulty in the interpretation of agronomic research, caused by the extreme local soil variability which characterizes Sahelian coversands. We actually exploit soil variability by using novel non-parametric techniques for data exploration in combination with spatial methods of parametric model estimation. Apart from N, P and K, the effects of surface crusting, local topography, manure levels, farmer behaviour and spatial dependence are taken into account, since these may confound the true effects of N, P and K. A quadratic formulation conforms best to the data and explains 81 percent of the yield variation. The equation highlights the importance of interactions among variables and thus confirms the possible impact of native soil conditions on the outcome of fertilizer treatments in experimental research. The results of much earlier, multi-year, research are confirmed remarkably well by this single year study. In addition, a spatially explicit assessment on the crop response to increasing nutrient levels highlights that blanket fertilizer applications are inefficient, because yield increases in some places will be accompanied by yield decreases at other sites. Cash-constrained farmers therefore have to resort to precision farming techniques to maximize returns from minimal external input packages. However, a large part of the good explanation of millet yield variability over space derives from spatial autocorrelation, and not directly from topsoil N, P and K. This calls for further research on the factors that affect millet yield and on the characterization and classification of sites, followed by experimental work to design site-specific fertilizer technologies.