Summary: The present work is a sequel to a recent one published on this journal where the superiority of ‘radial design’ to compute the ‘total sensitivity index’ was ascertained. Both concepts belong to sensitivity analysis of model output. A radial design is the one whereby starting from a random point in the hyperspace of the input factors one step in turn is taken for each factor. The procedure is iterated a number of times with a different starting random point as to collect a sample of elementary shifts for each factor. The total sensitivity index is a powerful sensitivity measure which can be estimated based on such a sample. Given the similarity between the total sensitivity index and a screening test known as method of the elementary effects (or method of Morris), we test the radial design on this method. Both methods are best practices: the total sensitivity index in the class of the quantitative measures and the elementary effects in that of the screening methods. We find that the radial design is indeed superior even for the computation of the elementary effects method. This opens the door to a sensitivity analysis strategy whereby the analyst can start with a small number of points (screening-wise) and then - depending on the results - possibly increase the numeral of points up to compute a fully quantitative measure. Also of interest to practitioners is that a radial design is nothing else than an iterated ‘One factor At a Time’ (OAT) approach. OAT is a radial design of size one. While OAT is not a good practice, modelers in all domains keep using it for sensitivity analysis for reasons discussed elsewhere [A. Saltelli and P. Annoni, How to avoid a perfunctory sensitivity analysis, Environmental Modelling and Software 25, 1508–1517 (2010)]. With the present approach modelers are offered a straightforward and economic upgrade of their OAT which maintain OAT’s appeal of having just one factor moved at each step.