A cognitive radio system requires the QoS of the primary user maintained while the spectrum allocated to the primary user is used by the Secondary user. The primary user in such cognitive radio system may use a queue to store packet during transmission. In such a system the stability of the queue has to be ensured. This sharing of available spectrum may happen through any of the modes of operation such as joint interweave-underlay mode or only-interweave mode. In joint interweave-underlay mode, secondary user transmits when primary user is absent and transmits adaptively when the primary user is present. In the Joint Interweave-underlay mode, the role of the interference constraint on the secondary user transmit power is of vital importance. Hence in this paper, we use the technique of adaptive packet spreading in time to increase achievable packet throughput along with interference constraints on secondary user transmit power. We present the method and provide the simulation results and analyze them for different channel conditions.