To achieve high-speed (giga-bit) connectivity for short-range wireless multimedia applications, the millimeter-wave (mmWave) wireless personal area networks with directional antennas are gaining increased interest. Due to the use of directional antennas and mmWave communications, the probability of non-interfering transmissions increases in a localized region. Network throughput can be increased immensely by the concurrent time allocation of non-interfering transmissions. The problem of finding optimum time allocation for concurrent transmissions is an NP-hard problem. In this paper, we propose two enhanced versions of previously proposed multi-hop concurrent transmission (MHCT) schemes. To increase network capacity, the proposed schemes efficiently make use of the free holes in the time-allocation map of the MHCT scheme; thus, making it more compact.