This paper investigates the problem of joint optimization of subcarrier selection and power allocation for a dual-functional radar-communications (DFRC) system, which is capable of fulfilling both radar and communications applications. The primary aim of the proposed strategy is to reduce the power consumption of a DFRC system by jointly selecting the best subcarriers for radar and communications subsystems respectively and assigning the optimal illumination power on the corresponding subcarriers, while a certain mutual information (MI) for target estimation, a predefined data information rate (DIR) for information transferring, and a given number of subcarriers allocated for radar application are met. The resulting problem is built as a two-variable non-convex and solved by cyclic minimization algorithm (CMA) incorporating Karush-Kuhn-Tuckers (KKT) conditions. Finally, some simulation results validate that the achievable LPI performance of the DFRC system can effectively be enhanced by exploiting the presented strategy.