This paper considers the problem of Base Station power minimization in downlink Orthogonal Frequency Division Multiple Access (OFDMA) systems. It aims at providing new solutions for the reduction of the total energy consumption. Such solutions rely on joint subcarrier and power allocation, under the constraints of requested per-user data rate. Practical results show that the proposed techniques allow a significant decrease of transmission power with an affordable complexity, compared to well-referenced methods from the literature.