In directional modulation (DM) networks, two practical random-subcarrier-selection (RSS) methods are proposed to transmit confidential message to the desired user per orthogonal frequency division multiplexing (OFDM) symbol with only single receive power peak formed by constructing random subcarrier set and performing a randomization procedure. This scheme completely addresses the crucial problem facing secure precise wireless transmission (SPWT), how to achieve the SPWT per OFDM symbol while the traditional SPWT holds only in the statistically average sense. Several necessary conditions for SPWT per OFDM is derived and proposed: random, distributed, and distinct subcarrier spacing pattern mapped onto transmit antenna array. Two random subcarrier index sets, quadratic subcarrier set (QSS) and prime subcarrier set (PSS), are constructed. Subsequently, a random metric is defined, and a randomization procedure (RP) is proposed. Its detailed process includes the following steps: integer mod, ordering, blocking, and block interleaving (BI) where BI is repeated until the random metric is greater than the predefined value. This yields a single high energy main peak (SHEMP) at the desired position with other positions, outside the main peak, harvesting only weak receive energy seriously corrupted by AN. Simulation results confirm that our proposed two methods, QSS plus RP and PSS plus RP, perform significantly better than conventional methods such as linear subcarrier set (LSS) plus RP. They actually form a SHEMP at desired position, and generate only extremely small leakage outside the main peak.