We investigate transmission energy minimization via optimizing wireless relay selection in orthogonal-frequency-division multiple access (OFDMA) networks. We take into account the impact of the load of cells on transmission energy. We prove the NP-hardness of the energy-aware wireless relay selection problem. To tackle the computational complexity, a partial optimality condition is derived for providing insights in respect of designing an effective and efficient algorithm. Numerical results show that the resulting algorithm achieves high energy performance.