We consider the classic continuous-review N-stage serial inventory system with a homogeneous Poisson demand arrival process at the most downstream stage (Stage 1). Any shipment to each stage, regardless of its size, incurs a positive fixed setup cost and takes a positive constant leadtime. The optimal policy for this system under the long-run average cost criterion is unknown. Finding a good worst-case performance guarantee for this problem remains an open problem. We tackle this problem by introducing a class of modified echelon (r, Q) policies that do not require Q_{i 1}/Q_i to be a positive integer: Stage i 1 ships to Stage i based on its observation of the echelon inventory position at Stage i; if it is at or below r_i and Stage i 1 has positive on-hand inventory, then a shipment is sent to Stage i to raise its echelon inventory position to r_i Q_i as close as possible. We construct a heuristic policy within this class of policies, which has the following features: First, it has provably primitive-dependent performance bounds. In a two-stage system, the performance of the heuristic policy is guaranteed to be within (1 K_1/K_2) times of the optimal cost, where K_1 is the downstream fixed cost and K_2 is the upstream fixed cost. We also provide an alternative performance bound, which depends on efficiently-computable optimal (r, Q) solutions to N single-stage systems, but tends to be tighter. Second, the heuristic is simple, efficiently computable and numerically performs well, likely to even outperform the optimal integer-ratio echelon (r,Q) policies when K_1 is dominated by K_2. Third, the heuristic is asymptotically optimal, as we take some dominant relationships, between the setup or holding cost primitives at an upstream stage and its immediate downstream stage, to the extreme, e.g., when h_2/h_1\rightarrow0, where h_1 is the downstream holding cost parameter and h_2 is the upstream holding cost parameter
