The article deals with the types of speech influence, their usage in modern media discourse and the problem of social distrust caused by manipulative technologies. In the author's opinion, fearful public mood is the product of anti-rhetorical activity associated with the lack of public awareness of the main type of speech influence -persuasion, in which argumentation is addressed to critical analysis. Emphasis is put on the prospects of rhetoric that has always considered not only the text but the speech situation and cognitions as well. Rhetoric has always been discursive and it was the first science to observe the language with respect to speech influence. Integrative character of rhetoric was the reason why various sciences explored rhetorical heritage that later became their integral part. At the same time, rhetoric itself was not virtually being developed and at this stage of speech development, when investigating speech influence, it is necessary to combine different aspects, rhetorical and cognitivediscursive in particular. Consideration is taken of cognitive-rhetorical arguments, namely, presuppositional fund of communicants. A more profound assessment of a perceiving party can be done by using the methods of cognitive linguistics that studies the relation between the structure of cognition and language units. With that in mind, for argumentation to be successful it is necessary to study the system of adressee's presuppositions and thereafter construct a dialogue with him involving the arguments most suitable in each specific case. Making logical connections more open and using rhetorical presuppositional fund make it possible for the communicant to persuade the opponent and to disclose his dishonest moves.