This paper deals with yield mapping on the basis of monitor yield data. Every value of the yield map is determined by fitting paraboloid yield surface textures on floating neighbourhoods, but in a robust way so that the influence of outliers is bounded or completely annihilated. The neighbourhood used for fitting the paraboloid cone looks like a huge butterfly flying along the harvest track. In order to find its optimal size and shape, an experiment was conducted where measured yield values from a plot combine (true values) were obtained, as well as yield monitor data from a commercial combine with a wider head which then harvested the same stretch again! Both yields are expressed as a percentage of its median. The yield map is considered to have been optimised if the sum of squares of deviations between the true plot values and the corresponding yield map values has been minimised. To this end, an unusually large neighbourhood proved necessary, with the result that the best achievable yield map appears to be very smooth.