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Despite almost two decades of research, multiple challenges remain unresolved in Cognitive Radio (CR) scenarios, especially the fundamental problem of reliable spectrum sensing. Hence we propose a channel partitioning scheme (CPS) based CR relying on realistic imperfect spectrum sensing. The channels licensed to the primary user (PU) are partitioned into two sets. Channels in one of the sets are exclusively reserved for the PU, while those in the other can be accessed by both the PU and the secondary user (SU) after spectrum sensing. The PU prioritizes its transmissions over the two sets by first transmitting using the channels in the reserved set and then moves on to the unreserved set, if required. It is shown that this simple policy significantly improves the overall detection performance as well as the simultaneous achievable rates and reduces the overhead associated with sensing.