Recent years have witnessed an increased interest, by competition agencies, in assessing the competitive effects of partial acquisitions. We propose a generalization to a partial horizontal acquisition setting of the two most traditional indicators used to screen unilateral anti-competitive effects: the Helfindahl- Hirschman Index and the Gross Upward Price Pressure Index. The proposed generalized indicators can deal with all types of acquisitions that may lessen competition in the industry: acquisitions by owners that are internal to the industry (rival firms) and engage in cross-ownership, as well as acquisitions by owners that are external to the industry and engage in common-ownership. Furthermore, these indicators can deal with direct and indirect acquisitions, which may or may not correspond to control, and nest full mergers as a special case. We provide an empirical application to several acquisitions in the wet shaving industry. The results seem to suggest that (i) a full merger induces higher unilateral anti-competitive effects than a partial controlling acquisition involving the same firms, (ii) a partial controlling acquisition induces higher unilateral anti-competitive effects than a partial non-controlling acquisition involving the same firms and the same financial stakes, and (iii) an acquisition by owners that are internal to the industry induces higher unilateral anti-competitive effects than an acquisition (involving the same firms and the same stakes) by external owners that participate in more than one competitor firm. JEL Classification: L13, L41, L66 Keywords: Antitrust, Partial Horizontal Acquisitions, Oligopoly, Screening Indicators, HHI, GUPPI