This article focuses on grammatical constructions that attenuate or eliminate the expression of agency in Russian, using the frameworks of Radical Construction Grammar and Cognitive Grammar. Emphasis is on the organization of these constructions in larger networks of related personal and impersonal constructions, with impersonal constructions as peripheral members of the system. More specifically, we compare the role of the dative case in impersonal constructions containing a finite verb and an infinitive and demonstrate that there are two such constructions, which has implications for the concepts of main verb-hood and agentivity. This type of nuanced analysis takes into account factors such as case semantics and relationships among constructions in assessing how agency is assigned or avoided in Russian impersonal constructions, hence makes it possible to tease apart the differences between two impersonal constructions that appear identical in structure.