In secure precise 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 statistically average sense. Several necessary conditions for SPWT per OFDM is derived and proposed: randomly distributed, sparse, and distinct subcarrier distance between two pair of adjacent antennas. Two random subcarrier sets (RSSs), quadratic subcarrier set (QSS) and prime subcarrier set (PSS), are constructed, where the former means the subcarrier index associated with any antennas is the square of antenna index, and the latter implies that the subcarrier indices over all antennas are prime numbers. Subsequently, following those conditions for SPWT per OFDM, a random factor is defined, and a randomization procedure (RP) is proposed. Its detailed process includes the following steps: integer mod, ordering, blocking, and block interleaving where BI is repeated until the random factor is greater than the predefined threshold. This yields a single main receive energy peak (SMREP) at the desired position with other positions, outside the SMREP, harvesting only weak receive energy seriously corrupted by AN.