We compare several adaptive design strategies using a data set of 223 M2AX family of compounds for which the elastic properties [bulk (B), shear (G), and Young's (E) modulus] have been computed using density functional theory. The design strategies are decomposed into an iterative loop with two main steps: machine learning is used to train a regressor that predicts elastic properties in terms of elementary orbital radii of the individual components of the materials; and a selector uses these predictions and their uncertainties to choose the next material to investigate. The ultimate goal is to obtain a material with desired elastic properties in as few iterations as possible. We examine how the choice of data set size, regressor and selector impact the design. We find that selectors that use information about the prediction uncertainty outperform those that don't. Our work is a step in illustrating how adaptive design tools can guide the search for new materials with desired properties.