The article introduces a new method for designing auctions that help buyers acquire services within a strict budget. Unlike previous randomized auctions, the new method uses deterministic clock auctions, which are more practical and efficient. These auctions ensure fairness, transparency, and privacy for both buyers and sellers. The key finding is that the new auctions outperform previous ones by achieving better results for different types of valuation functions, such as submodular and subadditive valuations. This research provides a significant advancement in the field of budget-feasible procurement auctions.