Under normal circumstances wireless cellular networks provide adequate coverage and capacity. However in case of site failures, due to for example an earthquake or flooding, it is important to quickly resolve the resulting coverage and/or capacity problem. To achieve this goal, we investigate the joint use of dynamically deployed drone-mounted base stations (DBSs) and a cell outage compensation (COC) mechanism. With COC the surrounding, still operational, cells adjust their configuration to mitigate the performance degradation. We demonstrate that these two approaches can work well together and complement each other in the sense that while COC on its own is usually unable to restore the performance to its original level, it can help to significantly reduce the number of DBSs required to achieve this. In particular, in urban scenarios we observe a reduction in the number of DBSs to be deployed by up to 40%.