Given a finite set E of cardinality, say, N and a map ƒ:P(E) → {−∞}, we define a sequence e₁, …, e_N of elements of E to be ƒ-greedy if e_i {e₁, …, e_i−1} and ƒ({e₁, …, e_i}) ≥ ƒ({e₁, …, e_i−1} {e}) for all i {1, …, N} and all e E{e₁, …, e_i−1}. In addition, for any map η : E → we put ƒ_η(x) ƒ(x) + Σ_exη(e) for all x E, and we define ƒ to be a well-layered map if for every η : E →, every ƒ_η-greedy sequence e₁, …, e_N E and every layer P_i(E) {y E #y = i} (i = 0, …, N) we have ƒ_η({e₁, …, e_i}) = max{ƒ_η(y) y P_i(E)}. In this note, we characterize well-layered maps by some appropriate quantified version of the greedoid exchange condition or—equivalently—by some appropriate greedoidal version of the quantitative relations defining valuated matroids and valuated Δ-matroids, respectively.