Genetic Improvement (GI) uses search-based optimisation algorithms to automatically improve software with respect to both functional and non-functional properties. Our previous work showed that Regression Test Selection (RTS) can help speed up the use of GI and enhance the overall results while not affecting the software system’s validity. This article expands upon our investigation by answering further questions about safety and applying a GI algorithm based on Local Search (LS) in addition to the previously explored Genetic Programming (GP) approach. Further, we extend the number of subjects to 12 by analysing five larger real-world open-source programs. We empirically compare two state-of-the-art RTS techniques combined with GP and LS for these 12 programs. The results show that both RTS techniques are safe to use and can reduce the cost of GI by up to 80% and by 31% on average across programs. We also observe that both search-based algorithms impact the effectiveness gains of GI differently, and that various RTS strategies achieve differing gains in terms of efficiency. These results serve as further evidence that RTS must be used as a core component of the GI search process to maximise its effectiveness and efficiency.