The bottleneck in a production-inventory network is commonly taken to be the facility that most limits flow through the network and thus the most highly utilized facility. A further connotation of “bottleneck,” however, is the facility that most constrains system-wide performance or the facility at which additional resources would have the greatest impact. Adopting this broader sense of the term, we look for fill-rate bottlenecks: facilities in a production-inventory network that most constrain the system-wide fill rate (the proportion of demands filled within a fixed delivery leadtime) or facilities at which either additional production capacity or additional inventory would have the greatest impact on the fill rate. We consider systems in which various components are produced through a series of stages holding intermediate inventories and are then assembled into finished goods to meet external demands. With each station in the network we associate precise measures of the station's propensity to constrain the fill rate. We call a station with a minimal measure a fill-rate bottleneck and justify this label both theoretically and numerically. Examples show that even the least utilized facility can be a fill-rate bottleneck. Unlike utilization, our bottleneck criteria capture information about process variability.