Greek κρατύς and cognates (κράτος, κρατερός, etc.) are related to Vedic krátu- ‘resolve’ and Avestan xratu- ‘[guiding] intellect’. The cumulative phraseological evidence supports this etymological proposal: in at least ten cases, Greek personal names and phrasemes exhibiting a cognate of κρατύς (that is, κράτος and compounds with first member κρατ[α]ι-) combine with terms whose Indo-Iranian linguistic cognates are joined with Vedic krátu- and Avestan xratu-. Furthermore, Indo-Iranian expressions, in which Vedic krátu- and its compounds are referred to a god as attributes, are structurally comparable to Greek κρατὺς Ἀργεϊφόντης. Since Ἀργεϊφόντης is likely to reflect ‘shining (cf. Greek φαίνω) with whiteness/brightness (ἀργει-)’, it is possible to identify Vedic phraseological matches for the Greek formula, namely expressions in which Vedic krátu- and its derivative krátumant- combine with the notion of ‘shining widely’, Vedic ví-bhā (Vedic bhā being a linguistic congener of φαίνω). The phraseological correspondence between Vedic krátu- … agní- ‘Agni, [endowed with] resolve’, and κρατὺς Ἀργεϊφόντης ‘Argeiphontes, endowed with superior might (κράτος)’ may be added to the dossier of common phraseology which the Greek god shares with the Old Indic fire-deity.