Despite its recent introduction in literature, the Best–Worst Method (BWM) is among the most well-known and applied methods in Multicriteria Decision-Making. The method can be used to elicit the relative importance (weight) of the criteria as well as to get the priorities of the alternatives on the criteria at hand. In this paper, we will present an extension of the method, namely, the parsimonious Best–Worst-Method (P-BWM) permitting to apply the BWM to get the priorities of the alternatives in case they are in a large number. At first, the Decision-Maker (DM) is asked to give a rating to the alternatives under consideration; after, the classical BWM is applied to a set of reference alternatives to get their priorities used to compute, then, the priorities of all the alternatives under consideration. We propose also a procedure to select reference alternatives, possibly in cooperation with the DM, providing a well-distributed coverage of the rating range. The new proposal requires the DM a fewer number of pairwise comparisons than the original BWM. Another contribution of the paper is related to the comparison between BWM, P-BWM, the Analytic Hierarchy Process (AHP), and the parsimonious AHP in terms of the amount of preference information provided by the DM in each method to apply it. In addition to the standard approach, we propose one alternative way of inferring the priority vectors in BWM and P-BWM based on the barycenter of the space of alternatives priorities compatible with the preferences given by the DM. Finally, an experiment with university students has been conducted to test the new proposal. Results of the experiments show that P-BWM performs better than BWM in terms of capability to represent the DM's preferences and the difference between the results of the two methods is significant from the statistical point of view. The new proposal will permit to use the potentialities of the BWM to get the alternatives’ priorities in real-world decision-making problems where a large number of alternatives must be taken into account.