While all Nakh-Daghestanian languages show ergative–absolutive patterns of case assignment and gender/number agreement, many languages have sentences containing imperfective transitive predicates with both A and P in the absolutive case. In these bi-absolutive constructions, A is generally topicalized whereas P is pragmatically demoted. Bi-absolutive constructions show a number of structural properties (e.g. word-order constraints) which are absent in ergative constructions, but the precise nature and number of these constraints differs from language to language. In this article I offer the first in-depth analysis of bi-absolutive constructions, describing also the range of variation in these constructions in the Nakh-Daghestanian languages. I argue that the traditional biclausal analysis fails to explain all properties of these constructions. Other structural approaches such as anti-passivization and noun-stripping are also rejected as inadequate. Instead, I propose to analyze bi-absolutive constructions in the wider context of information-restructuring devices.