This work investigates the efficiency of tuned inerter dampers (TIDs) in controlling seismic response of two adjacent buildings and the pounding distance between them. Pervious research on this subject has shown that installing TIDs in every floor of one of the buildings and coupling each floor of the two buildings with additional inerters (CS1) provides the best control performance. Some potential drawbacks of this solution are the large number of control devices used and practical difficulties associated with sharing inerters between adjacent buildings. To overcome these drawbacks, we propose a new configuration of TMDIs, called here as CS2. The proposed configuration makes use of much fewer control devices than CS1 and does not require coupling between the two buildings. Contrary to the findings of the published literature, we show that uncoupled control systems can be configured and tuned to be more effective than coupled systems. This superior performance of the proposed system is primarily due to the different arrangement of inerter devices in CS2 compared to that in CS1. In CS2, the inerters are connected to TMD masses rather than to the adjacent floors as is done in CS1. Performance assessment of the proposed solution and its comparison with CS1 is carried out through two numerical examples and several ground motions covering a large range of amplitude and frequency content. In the first numerical example, the adjacent buildings are of different heights but similar fundamental periods of vibration. In the second one, the buildings are of the same height but different fundamental periods of vibrations. These two examples cover cases of adjacent buildings facing lower and higher risk of pounding, respectively. The proposed solution is found to be effective and better than existing TID configuration in both the numerical examples studied here.