Databases play a crucial role in storing and managing vast amounts of data in various organizations and industries. Yet the risk of database leakage poses a significant threat to data privacy and security. To trace the source of database leakage, researchers have proposed many database watermarking schemes. Among them, fake-tuples-based database watermarking shows great potential as it does not modify the original data of the database, ensuring the seamless usability of the watermarked database. However, the existing fake-tuple-based database watermarking schemes need to insert a large number of fake tuples for the embedding of each watermark bit, resulting in low watermark transparency. Therefore, we propose a novel database watermarking scheme based on fake tuples and sparse priority strategy, named SPSW, which achieves the same watermark capacity with a lower number of inserted fake tuples compared to the existing embedding strategy. Specifically, for a database about to be watermarked, we prioritize embedding the sparsest watermark sequence, i.e., the sequence containing the most `0' bits among the currently available watermark sequences. For each bit in the sparse watermark sequence, when it is set to `1', SPSW will embed the corresponding set of fake tuples into the database. Otherwise, no modifications will be made to the database. Through theoretical analysis, the proposed sparse priority strategy not only improves transparency but also enhances the robustness of the watermark. The comparative experimental results with other database watermarking schemes further validate the superior performance of the proposed SPSW, aligning with the theoretical analysis.