By cooperative spectrum sharing schemes, a primary network (PN) leases a part of the licensed band to a secondary network (SN). A secondary transmitter (ST) acts as a relay for the primary transmitter (PT) to improve the end-to-end link quality of the PN, and as a reward, the ST gets the opportunity to transmit its own data by superposition coding. In this paper, a new cooperative spectrum sharing (CSS) scheme taking into account malicious eavesdropping (wiretapping) by a PN is proposed. In such scheme, licensed band is a decoy to an SN to wiretap the secondary transmission. Thus, secrecy in secondary transmission becomes critical to the SN. To get achievable secrecy (data) rate in secondary transmission and to fulfill the duty as a relay for primary transmission, the SN looks for a smart power-allocation (SPA) parameter that satisfies both goals. SPA parameter alpha(smart) provides the target secrecy data rate, and the achieved data rate at the PN is greater than or equal to the data rate obtained by the direct transmission (DT). Considering a Rayleigh block-fading channel, the SPA parameter is evaluated for each secondary transmission. Details on the evaluation of the SPA parameter are presented, and theoretical outage probabilities of the PN and the SN are derived and validated by simulations.