This paper discusses two analyses of the Anaphor Agreement Effect (AAE, Rizzi 1990) in the light of novel data from Avar. By demonstrating that Avar anaphors trigger full, non-trivial agreement on the φ-probe, I argue that the Avar data instantiate a genuine exception to the AAE. I then compare two competing analyses of binding and the AAE: an account whereby anaphoric dependencies arise via the syntactic operation Agree ( Murugesan 2019), and a theory deriving the inability of the anaphors’ φ-features to trigger full agreement from the presence of additional structural layers inside the anaphors that render the features inaccessible ( Preminger 2019). I claim that the absence of the AAE in Avar is in line with the encapsulation analysis whereas the Agree-based analysis is unsuccessful.