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In this work, we propose a transmission strategy for secondary users (SUs) within a cognitive radio network where primary users (PUs) exploit variable-rate variable-power modulation. By monitoring the PU's transmissions, the SU adjusts its transmit power based on the gap between the PU's received effective signal-to-noise power ratio (SNR) and the lower SNR boundary for the modulation mode that is being used in the primary link. Thus, at the SU's presence, the PU's quality of service (QoS) is guaranteed without increasing its processing complexity thanks to no interference cancellation required in the PU's operation. To demonstrate the advantage of our proposed transmission strategy, we analyze the secondary user's achievable data rate by taking into account different transmission capabilities for the secondary transmitter. The corresponding numerical results not only prove the validity of our derivations but also provide a convenient tool for the network design with the proposed transmission strategy.