Abstract Andi (Nakh-Daghestanian; Russia) displays a typologically remarkable phenomenon: adverbs of numerous morphological and functional types inflect for agreement with a clause-level controller. To the extent that adverb agreement has been observed elsewhere, it is commonly taken to signal that the items involved are semantically oriented towards the participants they agree with, aligning the phenomenon with secondary predication. This paper demonstrates that Andi works differently: the widespread clausal agreement seen on Andi adverbs is insensitive to participant orientation. While agreement exponence on adverbs is morphologically complex, a simple structural principle (modelled here in Minimalist terms) ensures that clause-level agreement is always with the absolutive-case argument. The Andi facts thus provide evidence for a typological distinction between those languages where clausal agreement on adverbs can serve a semantic function and those where it cannot. A potential challenge is posed by the exceptional “biabsolutive” construction, where both subject and object appear in absolutive case and either may control adverb agreement, suggesting a role for some additional non-structural factor. However, on independent grounds this paper identifies the two arguments as belonging to distinct structural layers; this apparent flexibility in controller choice merely reflects the ability of certain adverbs to modify either layer.