This chapter presents novel techniques to drastically reduce the search space in optimal quantum circuit mapping. These observations are backed by formal proofs using group theory, demonstrating that optimality is maintained despite the reduced search space. Experimental results show speed-ups of up to three orders of magnitude compared to exploring the full search space. Many previously intractable instances can now be mapped optimally within minutes. The proposed techniques are available as part of the open-source MQT QMAP tool, making optimal quantum circuit mapping more practical for larger circuits and architectures.