  We present a strong upper bound on the number k(B) of irreducible characters
of a p-block B of a finite group G in terms of local invariants. More
precisely, the bound depends on a chosen major B-subsection (u,b), its
normalizer N_G(\langle u\rangle,b) in the fusion system and a weighted sum of
the Cartan invariants of b. In this way we strengthen and unify previous bounds
given by Brauer, Wada, K\"ulshammer--Wada, H\'ethelyi--K\"ulshammer--Sambale
and the present author.
