Classical CCR and BCC models follow the principle of best possible self-assessment of each DMU compared to other economic entities. Another, more objective and peer-oriented approach is based on the determination of so called cross-efficiencies. Here, each DMU is evaluated by a peer’s optimal weights in a more objective way. Whilst under the assumption of constant returns of scale (CRS), calculation of cross-efficiencies is independent of input or output orientation, this is not the case for variable returns of scale (VRS). In this case, some input-oriented cross-efficiencies may even be negative. However, what does this entail in authentic situations? A meaningful application of this, an example taken from the European Health System, convincingly illustrates this phenomenon. Resulting from this, recommendations as to how to overcome negative DMUs' inefficiencies from a given peer's viewpoint will be discussed.