Virtual screening is a commonly used process to search for feasible drug candidates from a huge number of compounds during the early stages of drug design. As the compound database continues to expand to billions of entries or more, there remains an urgent need to accelerate the process of docking calculations. Reuse of calculation results is a possible way to accelerate the process. In this study, we first propose yet another virtual screening-oriented docking strategy by combining three factors, namely, compound decomposition, simplified fragment grid storing k-best scores, and flexibility consideration with pregenerated conformers. Candidate compounds contain many common fragments (chemical substructures). Thus, the calculation results of these common fragments can be reused among them. As a proof-of-concept of the aforementioned strategies, we also conducted the development of REstretto, a tool that implements the three factors to enable the reuse of calculation results. We demonstrated that the speed and accuracy of REstretto were comparable to those of AutoDock Vina, a well-known free docking tool. The implementation of REstretto has much room for further performance improvement, and therefore, the results show the feasibility of the strategy. The code is available under an MIT license at https://github.com/akiyamalab/restretto.