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Most known DSA (Dynamic Spectrum Access) methods in wireless network aim at enhancing the total system utility. As such, spectrum wastage may arise when the system-wise optimal allocation falls outside the desired region for QoS provisioning. The goal of this paper is to develop QoS-aware distributed DSA schemes using a game-theoretic approach. We devise a DSA solution which provides QoS level within preset range to as many users as possible. For this, we define it as a price for QoS level to escape beyond the preset range. Our scheme increases the number of satisfied users by 30% while reducing power consumption by 11%, compared with a state-of-the-art algorithm which is developed for maximum system utility.