One of the most important historical sources of Antitrust was the attempt to contain and prevent “monopolizing”. The topic ever since has intrigued legal scholars and economists. The borderline between legitimate competitive activities and “abuse” of dominant undertakingsturned out not to be easy to draw. There is case law; but it clearly is notstraightforward to develop reliable general principles which would allow us to predict which conduct should and would be considered an abuse and which not. The present paper uses the economic concept of efficiency to show some of the difficulties. Its main thesis is that it is more the concept of dominance than the concept of abuse which may cause the difficulties.