The prominent Herfindahl-Hirschman index (HHI), yields a higher concentration level in response to any merger between firms, implying that any merger will decrease the social welfare. Although HHI is used by the Anti-trust Division of the U.S. Department of Justice (AD-DoJ), its merger implications are not fully embraced by the anti-trust authorities. We propose a class of concentration indices that is in line with the spirit of the AD-DoJ's merger policies and consider different theoretical models which indicate that the AD-DoJ is justified in allowing mergers especially among smaller firms, as they counter the market power of dominant firms.