Satisfying the Quality of Service (QoS) is often a challenge in cognitive radio networks, because they depend on opportunistic channel accessing. In this context, appropriate pricing of vacant channels that is linked to the preference in their allocation, is found to be useful. However, ambiguity on the possible price at which the channel would be allotted is still a concern. In this work, an auction mechanism in which maximum value of the bid is predefined is proposed. With this, users quote their bid values as per their needs of getting the channels, up to the predefined maximum allowed bid price. However, final price of allocation is decided based on the sum total demand from all the users and the availability of vacant channels. Performance of the system is found in terms of blocking probabilities of secondary users and revenues to primary users. The proposed system is found to yield similar quantum of revenues as that of the Generalized Second Price (GSP) auction, while offering much lesser blocking probabilities to high-priority users to satisfy their QoS requirements.