  An extended class of N=2 locally supersymmetric invariants with
higher-derivative couplings based on full superspace integrals, is constructed.
These invariants may depend on unrestricted chiral supermultiplets, on vector
supermultiplets and on the Weyl supermultiplet. Supersymmetry is realized
off-shell. A non-renormalization theorem is proven according to which none of
these invariants can contribute to the entropy and electric charges of BPS
black holes. Some of these invariants may be relevant for topological string
deformations.
