This paper studies the optimal policies for stochastic periodic-review inventory systems with general quantitydependent costs, where both fixed and unit costs decrease with the order quantity z. The cost structure is defined as (K 1 + c 1 z)1[0 < z < Q] + (K 2 + c 2 z)1[z ≥ Q], with K 1 ≥ K 2 and c 1 ≥ c 2. Managing inventory under this general nonlinear ordering cost has long been an open problem. Methodologically, we introduce a new technical property called (K, c, Q)increase. We show that the optimal policy is a state-dependent (s, S, X, Q) policy, which is also a (s, S)-type policy. Specifically, the finite-horizon policy exhibits characteristics of the (s, S) policy for higher and lower inventory levels. For medium inventory levels, we identify the corresponding critical points and the range of the optimal order quantities, which guide decisions on when to avoid ordering, when to place an order less than Q, or when to order more than Q. For the infinite-horizon case, we prove that the discount-optimal policy preserves the structure of the finite-horizon counterpart. We then focus on the c 1 = c 2 model, which considers only decreasing fixed costs. This special model not only satisfies the (K, c, Q)-increase property but also exhibits the bounded differences property, enabling us to derive more refined structural properties compared to the general model. Furthermore, its average-optimal policy maintains the discount-optimal structure through the vanishing discount approach. Regarding heuristic policies, we first analyze the performance of (s, S) policy in our model. Under bounded demand, we show that as Q grows sufficiently large, (s, S) policy becomes optimal for the finite-horizon problem and achieves asymptotic optimality for the infinite-horizon case. We propose the (s 1 , s 2 , Q) policy as another heuristic, which demonstrates effective performance across a large number of instances in numerical experiments.