We show that a very general hypersurface of degree \(d\) at least \(4\) and dimension at most \((d+1)2^{d-4}\) over a field of characteristic different from \(2\) does not admit a decomposition of the diagonal; hence it is neither stably nor retract rational, nor \(\mathbb A^1\)-connected. This improves earlier results of myself (2019) and Moe (2023). Joint work with Jan Lange.