This paper deals with the analysis of a single-location, multi-item inventory model for service tools, in which coupled demands and coupled returns occur. We distinguish multiple Poisson demand streams. Per stream there is a given set of tools that is requested per demand. We are interested in the order fill rates, i.e., the percentage of demands for which all requested tools are delivered from stock. Requested tools that are not on stock are delivered via an emergency channel. For the warehouse under consideration, they may be considered as lost sales. Delivered tools are returned to the warehouse after a deterministic return time, that is equal for all tools. We show that the full multi-item evaluation problem decomposes into evaluation problems for small sets of service tools. For the resulting subproblems, we develop three approximate models for the order fill rates, which are all based on Markovian models. One approximate model has appeared to give an underestimation in all computational tests, while the second approximate model has led to an overestimation in all instances tested. The last approximate model combines the other two. This approximate model is very accurate and can be computed efficiently for representative instances based on data from an Original Equipment Manufacturer with whom we collaborated for this research.