This paper aims to provide a novel construct that is based on data envelopment analysis (DEA) range adjusted measure (RAM) of efficiency and demonstrate its practical implementation by evaluating the financial performance of a sample of three upper-class contracting license (Classes 5–7) Greek construction firms. In a two-step framework, firm efficiency (i.e., composite indicators (CIs)) is produced firstly by means of RAM using single financial ratios, which are selected by grey relational analysis (GRA), and then Tobit regression is employed to model the CIs. In light of the results, only 4% of the sampled firms are efficient, and the firm ranking is consistent with the ranking of Grey Relational Grande (GRG) values produced by GRA. Moreover, the firms with a contracting license of the highest level (Class 7) appear not to be superior in efficiency to their counterparts that belong to Classes 5–6.