In cooperative spectrum sharing-based cognitive radio systems, the secondary user (SU) acts as a cooperator of the primary user (PU) to assist the PU's transmission and is allowed to simultaneously transmit at the same spectrum only if it is not harmful to the primary transmission. Here the authors studies a power minimising problem of the SU with real-time services for this system under constraints on the SU's quality-of-service requirement and guaranteeing the PU's instantaneous rate unchanged if the SU allocates part of its power for its own transmissions. Superposition coding (SC) is further employed by the SU to eliminate the interference caused by the PU. The problem is formulated as an optimisation problem. Owing to its high complexity, this problem is then converted into a single variable optimisation problem, and a greedy-based power minimisation method with low complexity is thus proposed. Numerical comparison shows that the proposed method can lead to reductions in the secondary transmission power of about 30 and 14% against for the non-SC one and the equal bit allocation-based one, respectively.