A methodology is presented for obtaining plasticity characteristics of bulk metallic materials from single run indentation data. It involves repeated FEM modelling, with the predicted outcome (load-displacement plot) being systematically compared with experiment. The “correct” property values are found by searching for the combination giving the maximum value for a “goodness of fit” parameter (g) measuring the agreement between experimental and predicted outcomes (ranging from 0 for no agreement to 1 for perfect agreement). A matrix of property values are used as input data for the FEM model. The key issue is that of promoting convergence on the “correct” parameter combination. It is becoming accepted that use of more than one indenter shape will assist in this operation and the paper includes an exploration of this issue. It is emphasized that the strain field beneath an indenter affects the relationship between stress-strain curve and load-displacement plot, so use of shapes that create different strain fields adds extra degrees of freedom that facilitate convergence. However, there are various problems associated with use of indenters having “sharp” points or edges, and a spherical shape is much preferred. It is highlighted here that, provided the indenter shape is not self-similar (so that the nature of the strain field changes with increasing penetration depth), analogous benefits to those arising from multiple shapes can be obtained by carrying out “g-screening” operations on multiple sections of a single load-displacement plot. This is an entirely novel approach that offers considerable promise for the tractable characterization of plasticity via a single indentation run with a spherical indenter. It has been employed in the present work to obtain values of three plasticity parameters from such a run for an extruded copper sample. In fact, the stress-strain curve for this material is not one that conforms closely to a simple analytical formulation, imposing a limit on the fidelity of the inferred stress-strain curve, but it is nevertheless shown that the proposed procedure is viable and potentially very accurate.