  We revisit the old result that biflat Banach algebras have the same cyclic
cohomology as $\mathbb C$, and obtain a quantitative variant (which is needed
in forthcoming joint work of the author). Our approach does not rely on the
Connes-Tsygan exact sequence, but is motivated strongly by its construction as
found in [Connes,1985] and [Helemskii,1992].
