We identify some shortcomings of the hypothetical monopolist definition (HMD) of the relevant market as set out in the 1992 U.S. Merger Guidelines and followed by competition regimes worldwide, and propose a rephrased version to give the HMD a greater scientific rigor. It is shown that market boundaries under the HMD depend significantly on supply-related factors (such as pre-merger competitive interaction and the shape of cost functions), contrary to the claim in the Guidelines that market definition focuses solely on demand substitution factors. We formulate two alternative definitions of relevant market that build on the same logic as the HMD but do depend only on demand factors.