New supersymmetric higher-derivative couplings: full N = 2 superspace does not count!

An extended class of N = 2 locally supersymmetric invariants with higher-derivative couplings based on full superspace integrals, i s constructed. These invariants may depend on unrestricted chiral supermultiplets, on vect or 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 con tribute to the entropy and electric charges of BPS black holes. Some of these invariant s may be relevant for topological string deformations.